@incollection{BGL19,
	title = {On Cacti and Crystals},
	volume = {330},
	pages = {19--72},
	booktitle = {Representations and Nilpotent Orbits of Lie Algebraic Systems},
	publisher = {Springer International Publishing},
	author = {Berenstein, A. and Greenstein, J. and Li, J.-R.},
	editor = {Gorelik, Maria and Hinich, Vladimir and Melnikov, Anna},
	date = {2019},
	doi = {10.1007/978-3-030-23531-4_2},
}

@misc{Ro21b,
	author = {I. Rodrigues},
	title = {A shifted Berenstein--Kirillov group and the cactus group},
	year = {2021},
	eprint = {2104.11799},
	eprinttype = {arxiv}
}



@misc{Az18,
      title={Skew RSK and coincidence of Littlewood-Richardson commutors}, 
      author={O. Azenhas},
      year={2018},
      eprint={1808.06095},
      archivePrefix={arXiv},
}


@misc{AsOg18,
    author = {S. Assaf and E. K. Oğuz},
    title = {A local characterization of crystals for the quantum queer superalgebra},
    eprint = {1803.06317},
    eprinttype = {arxiv},
    year = {2018}
}


@book{Sta99, 
place={Cambridge}, 
series={Cambridge Studies in Advanced Mathematics}, 
title={Enumerative Combinatorics, Volume 2 (with an Appendix by S. Fomin)}, 
DOI={10.1017/CBO9780511609589}, 
publisher={Cambridge University Press}, 
author={R. P. Stanley}, 
year={1999}, 
collection={Cambridge Studies in Advanced Mathematics}
}

@incollection{Kir01,
	Author = {A. N. Kirillov},
	Editor = {A. N. Kirillov,N. Liskova},
	Title = {Introduction to Tropical Combinatorics},
	booktitle  = {Physics and Combinatorics 2000},
	year = {2001},
	publisher = {World Scientific},
	pages = {82--150}
}

@article{Ro20a,
	author = {I. Rodrigues},
	title = {A cactus group action on shifted tableau crystals},
	year = {2020},
	journal = {Séminaire Lotharingien de Combinatoire -- FPSAC 2020,},
	volume = {84B}
}

@misc{Ro20b,
	author = {I. Rodrigues},
	title = {A cactus group action on shifted tableau crystals},
	year = {2020},
	eprint = {2007.07078},
	eprinttype = {arxiv},
}

@article{GHPS18,
    author = {M. Gillespie and G. Hawkes and W. Poh and A. Schilling},
    title = {Characterization of queer supercrystals},
	journal = {Journal of Combinatorial Theory, Series A},
	volume = {173},
	pages = {105235},
	year = {2020},
}


@article{Lusz91,
	author = {G. Lusztig},
	title = {Canonical bases arising from quantized enveloping algebras},
	journal = {II.Progr. Theoret. Phys. Suppl.},
	volume = {102},
	pages = {175--201},
	year = {1991},
}

@inproceedings{TY16,
author = {H. Thomas and A. Yong},
booktitle = {Schubert Calculus — Osaka 2012},
doi = {10.2969/aspm/07110475},
pages = {475--497},
publisher = {Mathematical Society of Japan},
title = {Cominuscule tableau combinatorics},
year = {2016},
}


@article{TY09,
	author = {H. Thomas and A. Yong},
	title = {A combinatorial rule for (co)miniscule Schubert calculus},
	journal = {Adv. Math.},
	volume = {222},
	number = {2},
	year = {2009},
	pages = {596--620},
}


@article{PY17,
	author = {O. Pechenik and A. Yong},
	title = {Genomic tableaux},
	journal = {J. Algebraic Combin.},
	volume = {45},
	number = {3},
	year = {2017},
	pages = {649--685},
}


@article{CGP16,
    author = {M. Chmutov and M. Glick and P. Pylyavskyy},
    title = {The Berenstein-Kirillov group and cactus groups},
	journal = {Journal of Combinatorial Algebra},
	year={2020},
	Volume = {4},
	number = {2},
	pages = {111--140},
}


@article{DJS03,
	Author={M. Davis and T. Januszkiewicz and R. Scott},
	Title={Fundamental groups of blow-ups},
	Journal={Adv. Math.},
	Volume={117},
	Year={2003},
	number={1},
	Pages={115--179}
}



@article{BK16,
	author = {A. D. Berenstein and A. N. Kirillov},
	title = {Cactus group and Gelfand-Tsetlin group},
	journal = {Res. Inst. Math. Sci. preprint},
	volume = {RIMS-1858},	
	year = {2016},
}


@article{BK95,
	author = {A. D. Berenstein and A. N. Kirillov},
	title = {Groups generated by involutions, Gelfand–Tsetlin patterns, and combinatorics of Young tableaux},
	journal = {Algebra i Analiz},
	volume = {7},
	year = {1995},
	number = {1},
	pages = {92--152},
}


@article{Dev99,
	Author={S. Devadoss},
	Title={Tessellations of Moduli Spaces and the Mosaic Operad},
	Journal={Contemporary Mathematics},
	Volume={239},
	Year={1999},
	Pages={91--114}
}


@article{Yo86,
	Author={A. Young},
	Title={On quantitative substitutional analysis},
	Journal={IX. Proc. London Math. Soc.},
	Volume={54},
	Number={2},
	Year={1952},
	Pages={219--253}
}

@article{HB86,
Author={H. Hiller and B. Boe},
Title={Pieri formula for $SO_{2n+1}/U_n$ and $Sp_n/U_n$},
Journal={Adv. Math.},
Volume={62},
Year={1986},
Pages={49--67}
}


@book{HoHu92,
Author={P. N. Hoffman and  J.F. Humphreys},
Title={Projective Representations of the Symmetric groups},
Publisher={Oxford University Press},
Year={1992}
}


@article{Joz89,
	Author = {T. Józefiak},
    Title = {Characters of projective representations of symmetric groups},
   JOURNAL = {Expositiones Math.},
    VOLUME = {7},
      YEAR = {1989},
     PAGES = {193--247}
}

@incollection{Sag90,
	Author = {B. Sagan},
	Editor = {D. Stanton},
	Title = {The ubiquitous Young tableau},
	booktitle  = {Invariant theory and Young tableaux},
	year = {1990},
	publisher = {Springer},
	pages = {262--298}
}



@article{LaSchu81,
	Author = {A. Lascoux and M.-P. Schützenberger},
    Title = {Le monoïde plaxique},
   JOURNAL = {Quad. “Ricerca Sci.”},
    VOLUME = {109},
      YEAR = {1981},
     PAGES = {129--156}
}



@article{Schu61,
	Author = {M.-P. Schützenberger},
    Title = {Quelques remarques sur une construction de Schensted},
   JOURNAL = {Canad. J. Math.},
    VOLUME = {13},
      YEAR = {1961},
     PAGES = {117--128}
}

@article{CNObij,
	Author = {S.-I. Choi and S.-Y. Nam and Y.-T. Oh},
     Title = {Bijections among combinatorial models for shifted Littlewood-
Richardson coefficients},
   JOURNAL = {J. Combin. Theory Ser. A},
  FJOURNAL = {Journal of Combinatorial Theory, Series A},
    VOLUME = {128},
      YEAR = {2014},
     PAGES = {56--83}
}


@article{CNO17,
	Author = {S.-I. Choi and S.-Y. Nam and Y.-T. Oh},
    Title = {Shifted tableau switchings and shifted Littlewood-Richardson coefficients},
    JOURNAL = {J. Korean Math. Soc.},
    VOLUME = {56},
    NUMBER = {4},
    PAGES = {947--984},
    year = {2019}
}

@misc{CNO17arxiv,
      title={Shifted tableau switchings and shifted Littlewood-Richardson coefficients}, 
      author={S.-I. Choi and S.-Y. Nam and Y.-T. Oh},
      year={2017},
      eprint={1701.08950},
      archivePrefix={arXiv},
}

@misc{CNOrev,
	Author = {S.-I. Choi and S.-Y. Nam and Y.-T. Oh},
	Title = {The shifted reversal and its applications},
	howpublished = {Preprint}
}


@incollection{Gi19,
 AUTHOR = {M. Gillespie},
 TITLE = {Variations on a Theme of Schubert Calculus},
booktitle = {Recent Trends in Algebraic Combinatorics},
 PUBLISHER={Association for Women in Mathematics Series, Springer},
 PAGES={115--158},
 YEAR={2019}
 }

@article{GLP17,
   author = {M. Gillespie and J. Levinson and K. Purbhoo},
    title = {A crystal-like structure on shifted tableaux},
    journal = {Algebraic Combinatorics},
    volume ={3},
    number ={3},
    year = {2020},
    pages = {693--725},
}


@article{GL19,
    author = {M. Gillespie and J. Levinson},
    title = {Axioms for shifted tableau crystals},
    journal = {The Electronic Journal of Combinatorics},
    volume = {26},
    year = {2019},
    number = {2}
}


@article{Stem90,
author = {J. R. Stembridge},
journal = {Banach Center Publications},
number = {2},
pages = {433-453},
title = {On symmetric functions and the spin characters of $S_n$},
volume = {26},
year = {1990},
}


@article{PV10,
author = {I. Pak and E. Vallejo},
title = {Reductions of Young tableau bijections},
journal = {SIAM Journal on Discrete Mathematics},
volume = {24},
number = {1},
pages = {113--145},
year = {2010},
}


@article{BSS96,
author = {G. Benkart and F. Sottile and J. Stroomer},
title = {Tableau switching: Algorithms and applications},
journal = {J. Combin. Theory Ser. A},
volume = {76},
year = {1996},
pages = {11--43}
}




@article{Stem89,
    AUTHOR = {Stembridge, J. R.},
     TITLE = {Shifted tableaux and the projective representations of
              symmetric groups},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {74},
      YEAR = {1989},
    NUMBER = {1},
     PAGES = {87--134}
}

@article{Sag87,
    AUTHOR = {Sagan, B.},
     TITLE = {Shifted tableaux, {S}chur {$Q$}-functions, and a conjecture of
              {R}. {S}tanley},
   JOURNAL = {J. Combin. Theory Ser. A},
  FJOURNAL = {Journal of Combinatorial Theory. Series A},
    VOLUME = {45},
      YEAR = {1987},
    NUMBER = {1},
     PAGES = {62--103}
}


@article{Haim89,
    AUTHOR = {Haiman, M.},
     TITLE = {On mixed insertion, symmetry and shifted Young tableaux},
   JOURNAL = {J. Combin. Theory Ser. A},
    VOLUME = {50},
      YEAR = {1989},
     PAGES = {196--225}
}

@article{Haim92,
    AUTHOR = {Haiman, M.},
     TITLE = {Dual equivalence with applications, including a conjecture of Proctor},
   JOURNAL = {Discrete Math.},
  FJOURNAL = {Discrete Mathematics},
    VOLUME = {92},
      YEAR = {1992},
     PAGES = {79--113}
}

@article{Sch1911,
    AUTHOR = {Schur, I.},
     TITLE = {Über die Darstellung der symmetrischen und der alternierenden Gruppe durch gebrochene lineare Substitutionen},
   JOURNAL = {J. Reine Angew. Math.},
    VOLUME = {139},
      YEAR = {1911},
     PAGES = {155--250}
}

@PhdThesis{Hala16,
    AUTHOR = {Halacheva, I.},
    TITLE = {Alexander type invariants of tangles, skew Howe duality for crystals and the cactus group},
    SCHOOL = {University of Toronto},
    YEAR = {2016}
}

@misc{Hala20,
	Author={Halacheva, I.},
	Title={Skew Howe duality for crystals and the cactus group},
	eprint = {2001.02262},
	eprinttype = {arxiv},
	year = {2020}
}

@PhdThesis{Wor84,
    AUTHOR = {Worley, D.},
    TITLE = {A Theory of Shifted Young Tableaux},
    SCHOOL = {MIT},
    YEAR = {1984}
}


@article{HenKam06,
    AUTHOR = {A. Henriques and J. Kamnitzer},
     TITLE = {Crystals and coboundary categories},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {132},
      YEAR = {2006},
    NUMBER = {2},
     PAGES = {191--216}
}



@incollection{Schu76,
    AUTHOR = {M.-P. Sch\"{u}tzenberger},
    editor = {D. Foata},
     TITLE = {La correspondance de Robinson},
 booktitle = {Combinatoire et repr\'{e}sentation du groupe sym\'{e}trique, Actes Table Ronde CNRS, Univ.
 Louis Pasteur, Strasbourg},
 Publisher={Springer},
      YEAR = {1976}
}

@article{Schu72,
Author = {M.-P. Schützenberger},
    Title = {Promotion des morphisms d'ensemble ordonnes},
   JOURNAL = {Disc. Math.},
    VOLUME = {2},
      YEAR = {1972},
     PAGES = {73--94}
}




@article {AzMaCo09,
    AUTHOR = {O. Azenhas and A. Conflitti and R. Mamede},
     TITLE = {Linear time equivalent Littlewood-Richardson coefficient maps},
   JOURNAL = {DMCTS Proceedings AK},
  FJOURNAL = {Discrete Mathematics & Theoretical Computer Science Proceedings},
    VOLUME = {FPSAC 2009},
      YEAR = {2009},
     PAGES = {127--144}
}


@article {AzMaCo20,
	AUTHOR = {O. Azenhas and A. Conflitti and R. Mamede},
     TITLE = {Involutions, their coincidence,  and complexity for symmetries of Littlewood-Richardson coefficients},
   JOURNAL = {In preparation},
	YEAR = {2020}
}

@book {BumpSchi17,
    AUTHOR = {Bump, D. and Schilling, A.},
     TITLE = {Crystal bases},
      NOTE = {Representations and combinatorics},
 PUBLISHER = {World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ},
      YEAR = {2017},
     PAGES = {xii+279},
   MRCLASS = {05-01 (05E10 14T05 17B10)},
  MRNUMBER = {3642318},
  DOI = {10.1142/9876}
}

@article{Kash95,
	author={M. Kashiwara},
	TITLE={On crystal bases},
	NOTE={Representations of groups (Banff, AB)},
	JOURNAL={CMS Conf. Proc.},
	NUMBER={6},
	PUBLISHER={Amer. Math. Soc., Providence, RI},
	PAGES={155--197},
	YEAR={1995}
}



@article{Kash94,
	Author = {M. Kashiwara},
	Title = {Crystal bases of modified quantized enveloping algebra},
	Journal = {Duke Math. J.},
	Volume = {73},
	Number = {2},
	Year = {1994},
	Pages = {383--413}
}


@book{JK81,
    AUTHOR = {Kerber, G. D. and James, A.},
     TITLE = {The Representation Theory of the Symmetric Group},
 PUBLISHER = {Addison-Wesley, Reading, MA},
      YEAR = {1981}
}

@book{Pr91,
	AUTHOR = {P. Pragacz},
	TITLE = {Algebro-geometric applications of Schur S- and Q-polynomials},
	NOTE = {Topics in invariant theory (Paris, 1989/1990)},
	Publisher = {Lecture Notes in Math.  Springer, Berlin},
	PAGES = {130--191},
	YEAR = {1991}
}

@misc{HaKaRyWe20,
	Author = {I. Halacheva and J. Kamnitzer and L. Rybnikov and A. Weeks},
	Title = {Crystals and monodromy of Bethe vectors},
	volume = {169},
	journal = {Duke Mathematical Journal},
	number = {12},
	publisher = {Duke University Press},
	pages = {2337 -- 2419},
	year = {2020}
}


@article{GLP19,
	Author = {M. Gillespie and  J. Levinson and  K. Purbhoo},
	Title = {Schubert curves in the orthogonal Grassmannian},
	eprint = {1903.01673},
	eprinttype = {arxiv},
	year = {2019}
}






@article{BeKn72,
	author = "E. Bender and D. Knuth",
	title = "Enumeration of plane partitions",
	journal = "Journal of Combinatorial Theory, Series A",
	volume = "13",
	number = "1",
	pages = "40--54",
	year = "1972",
}