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@book{assem2006elements,
	Author = {Assem, Ibrahim and Simson, Daniel and Skowro\'{n}ski, Andrzej},
	Date-Added = {2019-05-16 09:55:23 +0300},
	Date-Modified = {2019-05-16 09:57:28 +0300},
	Mrclass = {16G10 (16-02)},
	Mrnumber = {2197389},
	Mrreviewer = {Peter W. Donovan},
	Number = {65},
	Publisher = {Cambridge University Press, Cambridge},
	Series = {London Mathematical Society Student Texts},
	Title = {Elements of the Representation Theory of Associative Algebras. {V}ol. 1: Techniques of Representation Theory},
	Year = {2006},
	Bdsk-Url-1 = {https://doi-org.ezp.lib.unimelb.edu.au/10.1017/CBO9780511614309},
	Bdsk-Url-2 = {https://doi.org/10.1017/CBO9780511614309}}

@article{BZ,
	Author = {Berenstein, A. and Zelevinsky, A.},
	Journal = {Inventiones Mathematicae},
	Pages = {77--128},
	Title = {Tensor product multiplicities, canonical bases, and totally positive varieties},
	Volume = {143},
	Year = {2001}}

@book{billey2000singular,
	Author = {Billey, Sara and Lakshmibai, Venkatramani},
	Publisher = {Springer Science \& Business Media},
	Title = {Singular loci of Schubert varieties},
	Volume = {182},
	Year = {2000}}

@misc{einstein2013combinatorial,
	Author = {Einstein, D. and Propp, J.},
	Date-Modified = {2019-05-16 09:57:54 +0300},
	Eprint = {1310.5294},
	Eprinttype = {arxiv},
	Title = {Combinatorial, piecewise-linear, and birational homomesy for products of two chains},
	Year = {2018}}

@article{gabriel1972unzerlegbare,
	Author = {Gabriel, P.},
	Journal = {Manuscripta mathematica},
	Number = {1},
	Pages = {71--103},
	Publisher = {Springer},
	Title = {Unzerlegbare {D}arstellungen I},
	Volume = {6},
	Year = {1972}}

@incollection{gabriel1980auslander,
	Author = {Gabriel, P.},
	Journal = {Representation theory I},
	Pages = {1--71},
	Publisher = {Springer},
	Title = {Auslander--{R}eiten sequences and representation-finite algebras},
	Year = {1980}}

@article{gansner1981acyclic,
	Author = {Gansner, E. R.},
	Journal = {SIAM Journal on Algebraic Discrete Methods},
	Number = {4},
	Pages = {429--440},
	Publisher = {SIAM},
	Title = {Acyclic digraphs, {Y}oung tableaux and nilpotent matrices},
	Volume = {2},
	Year = {1981}}

@article{garver2017greene,
	Author = {Garver, A. and Patrias, R.},
	Journal = {arXiv preprint arXiv:1708.09720},
	Title = {Greene--{K}leitman invariants for {S}ulzgruber insertion},
	Year = {2017}}

@book{green2013combinatorics,
	Author = {Green, R. M.},
	Date-Modified = {2019-05-16 10:08:36 +0300},
	Number = {199},
	Publisher = {Cambridge University Press},
	Series = {Camb. Tracts Math.},
	Title = {Combinatorics of Minuscule Representations},
	Year = {2013}}

@article{greene1976structure,
	Author = {Greene, C. and Kleitman, D. J.},
	Journal = {Journal of Combinatorial Theory, Series A},
	Number = {1},
	Pages = {41--68},
	Publisher = {Elsevier},
	Title = {The structure of {S}perner {$k$}-families},
	Volume = {20},
	Year = {1976}}

@article{happel1985tilting,
	Author = {Happel, D.},
	Journal = {Proceedings of the London Mathematical Society},
	Number = {1},
	Pages = {21--55},
	Publisher = {Wiley Online Library},
	Title = {Tilting sets on cylinders},
	Volume = {3},
	Year = {1985}}

@article{keller2005triangulated,
	Author = {Keller, B.},
	Journal = {Documenta Mathematica},
	Pages = {551-581},
	Title = {On triangulated orbit categories},
	Volume = {10},
	Year = {2005}}

@incollection{kr,
	Author = {H. Kraft and C. Riedtmann},
	Booktitle = {Representations of algebras (Durham, 1985)},
	Pages = {109--145},
	Place = {Cambridge},
	Publisher = {Cambridge Univ. Press},
	Series = {London Math. Soc. Lecture Note Ser.},
	Title = {Geometry of representations of quivers},
	Volume = {116},
	Year = {1986}}

@article{farber2015interlacing,
	Author = {Farber, Miriam and Hopkins, Sam and Trongsiriwat, Wuttisak},
	Journal = {Journal of Combinatorial Theory, Series A},
	Pages = {339--371},
	Publisher = {Elsevier},
	Title = {Interlacing networks: Birational {R}{S}{K}, the octahedron recurrence, and {S}chur function identities},
	Volume = {133},
	Year = {2015}}

@misc{hopkins2014rsk,
	Author = {Hopkins, S.},
	Date-Modified = {2019-05-16 10:12:00 +0300},
	Note = {Unpublished notes},
	Title = {R{S}{K} via local transformations},
	Url = {http://www-users.math.umn.edu/~shopkins/docs/rsk.pdf},
	Year = {2014}}

@article{knuth1970permutations,
	Author = {Knuth, Donald},
	Journal = {Pacific Journal of Mathematics},
	Number = {3},
	Pages = {709--727},
	Publisher = {Mathematical Sciences Publishers},
	Title = {Permutations, matrices, and generalized {Y}oung tableaux},
	Volume = {34},
	Year = {1970}}

@article{pak2001hook,
	Author = {Pak, I.},
	Date-Modified = {2019-05-16 10:16:33 +0300},
	Journal = {S\'em. Loth. Comb.},
	Pages = {Art. B46f, 13 pp},
	Title = {Hook length formula and geometric combinatorics},
	Url = {https://www.mat.univie.ac.at/~slc/wpapers/s46pak.html},
	Volume = {46},
	Year = {2001}}

@article{peng1997root,
	Author = {Peng, L. and Xiao, J.},
	Journal = {Journal of Algebra},
	Number = {1},
	Pages = {19--56},
	Publisher = {New York: Academic Press,[1964-},
	Title = {Root categories and simple Lie algebras},
	Volume = {198},
	Year = {1997}}

@article{proctor1984bruhat,
	Author = {Proctor, R. A.},
	Date-Modified = {2019-05-16 10:17:19 +0300},
	Doi = {10.1016/s0195-6698(84)80037-2},
	Journal = {European J. Comb.},
	Number = {4},
	Pages = {331--350},
	Publisher = {Elsevier},
	Title = {Bruhat lattices, plane partition generating functions, and minuscule representations},
	Volume = {5},
	Year = {1984}}

@article{saks1980dilworth,
	Author = {Saks, Michael},
	Journal = {SIAM Journal on Algebraic Discrete Methods},
	Number = {2},
	Pages = {211--215},
	Publisher = {SIAM},
	Title = {Dilworth numbers, incidence maps and product partial orders},
	Volume = {1},
	Year = {1980}}

@article{bernstein1973coxeter,
	Author = {Bernstein, I. N. and Gel'fand, I. M. and Ponomarev, V. A.},
	Journal = {Russian mathematical surveys},
	Number = {2},
	Pages = {17--32},
	Publisher = {Turpion Ltd},
	Title = {Coxeter functors and {G}abriel's theorem},
	Volume = {28},
	Year = {1973}}

@article{kirillov1995groups,
	Author = {Kirillov, Anatolii Nikolaevich and Berenstein, Arkady D},
	Journal = {Algebra i Analiz},
	Number = {1},
	Pages = {92--152},
	Title = {Groups generated by involutions, Gelfand--Tsetlin patterns, and combinatorics of Young tableaux},
	Volume = {7},
	Year = {1995}}

@article{pylyavskyy:noncrossing,
	Author = {Pylyavskyy, Pavlo},
	Journal = {Annals of Combinatorics},
	Number = {3},
	Pages = {323--339},
	Publisher = {Springer},
	Title = {Non-crossing tableaux},
	Volume = {13},
	Year = {2009}}

@article{kac-infinite-i,
	Author = {Kac, V.},
	Journal = {Inventiones Mathematicae},
	Pages = {57--92},
	Title = {Infinite root systems, representations of graphs and invariant theory},
	Volume = {56},
	Year = {1980}}

@article{rush2013orbits,
	Author = {Rush, David B and Shi, XiaoLin},
	Journal = {Journal of Algebraic Combinatorics},
	Number = {3},
	Pages = {545--569},
	Publisher = {Springer},
	Title = {On orbits of order ideals of minuscule posets},
	Volume = {37},
	Year = {2013}}

@book{springer,
	Address = {Boston},
	Author = {T A Springer},
	Publisher = {Birkh\"auser},
	Title = {Linear algebraic groups},
	Year = {1998}}

@article{stembridge1996fully,
	Author = {Stembridge, J. R.},
	Journal = {Journal of Algebraic Combinatorics},
	Number = {4},
	Pages = {353--385},
	Publisher = {Springer},
	Title = {On the fully commutative elements of Coxeter groups},
	Volume = {5},
	Year = {1996}}

@misc{sulzgruberfull,
	Author = {Sulzgruber, Robin},
	Date-Modified = {2019-05-16 10:19:50 +0300},
	Eprint = {1710.09695},
	Eprinttype = {arxiv},
	Title = {Inserting rim-hooks into reverse plane partitions},
	Year = {2017}}

@article{sulzgruber2016building,
	Author = {Sulzgruber, R.},
	Journal = {arXiv preprint arXiv:1612.03922},
	Title = {Building reverse plane partitions with rim-hook-shaped bricks},
	Year = {2016}}

@book{stanley1999enumerative,
	Author = {Stanley, R. P.},
	Date-Modified = {2019-05-16 10:19:30 +0300},
	Publisher = {Cambridge University Press},
	Title = {Enumerative Combinatorics. Volume 2},
	Year = {1999}}

@article{stanley1971theory,
	Author = {Stanley, R. P.},
	Date-Modified = {2019-05-16 10:19:08 +0300},
	Doi = {10.1002/sapm1971503259},
	Journal = {Studies in Appl. Math.},
	Number = {2},
	Pages = {167--188},
	Publisher = {Wiley Online Library},
	Title = {Theory and application of plane partitions: Part 1},
	Volume = {50},
	Year = {1971}}

@article{hillman1976reverse,
	Author = {Hillman, A. P. and Grassl, R. M.},
	Date-Modified = {2019-05-16 10:09:45 +0300},
	Doi = {10.1016/0097-3165(76)90065-0},
	Journal = {J. Combin. Theory Ser. A},
	Number = {2},
	Pages = {216--221},
	Publisher = {Elsevier},
	Title = {Reverse plane partitions and tableau hook numbers},
	Volume = {21},
	Year = {1976}}

@article{morales2015hook,
	Author = {Morales, A. H. and Pak, I. and Panova, G.},
	Date-Modified = {2019-05-16 10:13:19 +0300},
	Doi = {10.1016/j.jcta.2017.09.002},
	Journal = {J. Combin. Theory Ser. A},
	Pages = {350--405},
	Publisher = {Elsevier},
	Title = {Hook formulas for skew shapes {I}. q-analogues and bijections},
	Volume = {154},
	Year = {2018}}

@article{gansner1981hillman,
	Author = {Gansner, E. R.},
	Date-Modified = {2019-05-16 10:04:43 +0300},
	Journal = {J. Combin. Theory Ser. A},
	Number = {1},
	Pages = {71--89},
	Publisher = {Elsevier},
	Title = {The {H}illman--{G}rassl correspondence and the enumeration of reverse plane partitions},
	Url = {https://doi.org/10.1016/0097-3165(81)90041-8},
	Volume = {30},
	Year = {1981}}

@misc{garver2017+,
	Author = {Garver, A. and Patrias, R. and Thomas, H.},
	Date-Modified = {2019-05-16 10:05:16 +0300},
	Eprint = {1812.08345},
	Eprinttype = {arxiv},
	Title = {Minuscule reverse plane partitions via quiver representations},
	Year = {2019}}

@book{gansner1977matrix,
	Author = {Gansner, Emden Robert},
	Title = {Matrix correspondences and the enumeration of plane partitions},
	Year = {1977}}

@article{ringel2008invariant,
	Author = {Ringel, C. M. and Schmidmeier, M.},
	Journal = {Journal f{\"u}r die reine und angewandte Mathematik (Crelles Journal)},
	Number = {614},
	Pages = {1--52},
	Publisher = {Walter de Gruyter},
	Title = {Invariant subspaces of nilpotent linear operators, {I}},
	Volume = {2008},
	Year = {2008}}

@article{wildberger2003minuscule,
	Author = {Wildberger, N. J.},
	Journal = {European Journal of Combinatorics},
	Number = {6},
	Pages = {741--757},
	Publisher = {Elsevier},
	Title = {Minuscule posets from neighbourly graph sequences},
	Volume = {24},
	Year = {2003}}