@unpublished {2007.07078, AUTHOR = {Rodrigues, In\^es}, TITLE = {An action of the cactus group of shifted tableau crystals}, NOTE = {Preprint, {\tt arXiv:2007.07078}}, eprint={2007.07078}, } @misc{Schu76, AUTHOR = {M.-P. Sch\"utzenberger}, 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{Kash95, author={M. Kashiwara}, TITLE={On crystal bases}, doi={10.1142/9876}, NOTE={Representations of groups (Banff, AB)}, JOURNAL={CMS Conf. Proc.}, NUMBER={6}, PUBLISHER={Amer. Math. Soc., Providence, RI}, PAGES={155--197}, YEAR={1995} } @article{CNO14, 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}, doi={10.1016/j.jcta.2014.07.007}, 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{GHPS18, author = {M. Gillespie and G. Hawkes and W. Poh and A. Schilling}, title = {Characterization of queer supercrystals}, eprint = {1809.04647}, eprinttype = {arxiv}, year = {2018} } @misc{GLP17, author = {M. Gillespie and J. Levinson and K. Purbhoo}, title = {A crystal-like structure on shifted tableaux}, eprint = {1706.09969}, eprinttype = {arxiv}, year = {2017} } @article{GL19, author = {M. Gillespie and J. Levinson}, title = {Axioms for shifted tableau crystals}, journal={Electr. J. Comb.}, doi={10.37236/8033}, volume = {26}, year = {2019}, number = {2} } @article {Stem89, AUTHOR = {Stembridge, J.}, TITLE = {Shifted tableaux and the projective representations of symmetric groups}, JOURNAL = {Adv. Math.}, doi={10.1016/0001-8708(89)90005-4}, 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}, doi={10.1016/0097-3165(87)90047-1}, NUMBER = {1}, PAGES = {62--103} } @article {Haim92, AUTHOR = {Haiman, M.}, TITLE = {Dual equivalence with applications, including a conjecture of Proctor}, JOURNAL = {Discrete Math.}, FJOURNAL = {Discrete Mathematics}, doi={10.1016/0012-365X(92)90368-P}, VOLUME = {92}, YEAR = {1992}, PAGES = {79--113} } @misc{Hala16, AUTHOR = {Halacheva, I.}, TITLE = {Alexander type invariants of tangles, skew Howe duality for crystals and the cactus group}, SCHOOL = {University of Toronto}, note="PhD thesis.", url={http://www.math.toronto.edu/ivahal/Halacheva_Iva_201611_PhD_thesis.pdf}, YEAR = {2016} } @misc{Wor84, AUTHOR = {Worley, D.}, TITLE = {A Theory of Shifted Young Tableaux}, note="PhD thesis.", url={https://dspace.mit.edu/handle/1721.1/15599}, SCHOOL = {MIT}, YEAR = {1984} } @article {HenKam06, AUTHOR = {A. Henriques and J. Kamnitzer}, TITLE = {Crystals and coboundary categories}, JOURNAL = {Duke Math. J.}, doi={0.1215/S0012-7094-06-13221-0}, FJOURNAL = {Duke Mathematical Journal}, VOLUME = {132}, YEAR = {2006}, NUMBER = {2}, PAGES = {191--216} } @misc{AsOg18, author = {S. Assaf and E. Oğuz}, title = {A local characterization of crystals for the quantum queer superalgebra}, eprint = {1803.06317}, eprinttype = {arxiv}, year = {2018} } @article {AzMaCo09, AUTHOR = {O. Azenhas and A. Conflitti and R. Mamede}, TITLE = {Linear time equivalent Littlewood-Richardson coefficient maps}, JOURNAL = {Discrete Mathematics and Theoretical Computer Science Proceedings}, VOLUME = {FPSAC}, YEAR = {2009}, PAGES = {127--144} } @book {BumpSchi17, AUTHOR = {Bump, D. and Schilling, A.}, TITLE = {Crystal bases}, doi={10.1142/9876 }, NOTE = {Representations and combinatorics}, PUBLISHER = {World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ}, YEAR = {2017}, }