Characterization of queer supercrystals

M Gillespie, G Hawkes, W Poh, A Schilling - Journal of Combinatorial …, 2020 - Elsevier
We provide a characterization of the crystal bases for the quantum queer superalgebra
recently introduced by Grantcharov et al. This characterization is a combination of local …

-Crystal Structure on Primed Tableaux and on Signed Unimodal Factorizations of Reduced Words of Type

T Hiroshima - Publications of the Research Institute for Mathematical …, 2019 - ems.press
Crystal basis theory for the queer Lie superalgebra was developed in Grantcharov et
al.(Trans. Amer. Math. Soc. 366, 2013, 457–489) and Grantcharov et al.(J. Europ. Math. Soc …

Highest weight crystals for Schur Q-functions

E Marberg, KH Tong - arXiv preprint arXiv:2112.02848, 2021 - arxiv.org
Work of Grantcharov et al. develops a theory of abstract crystals for the queer Lie
superalgebra $\mathfrak {q} _n $. Such $\mathfrak {q} _n $-crystals form a monoidal …

A crystal-like structure on shifted tableaux

M Gillespie, J Levinson… - Algebraic …, 2020 - alco.centre-mersenne.org
We introduce coplactic raising and lowering operators Ei, Fi, Ei, and Fi on shifted skew
semistandard tableaux. We show that the primed operators and unprimed operators each …

Axioms for shifted tableau crystals

M Gillespie, J Levinson - arXiv preprint arXiv:1807.03384, 2018 - arxiv.org
We give local axioms that uniquely characterize the crystal-like structure on shifted tableaux
developed in a previous paper by Gillespie, Levinson, and Purbhoo. These axioms closely …

Queer supercrystal structure for increasing factorizations of fixed-point-free involution words

T Hiroshima - arXiv preprint arXiv:1907.10836, 2019 - arxiv.org
We show that the set of increasing factorizations of fixed-point-free (FPF) involution words
has the structure of queer supercrystals. By exploiting the algorithm of symplectic shifted …

Bijecting hidden symmetries for skew staircase shapes

Z Hamaker, AH Morales, I Pak, L Serrano… - arXiv preprint arXiv …, 2021 - arxiv.org
We present a bijection between the set of standard Young tableaux of staircase minus
rectangle shape, and the set of marked shifted standard Young tableaux of a certain shifted …

On the Shifted Littlewood–Richardson Coefficients and the Littlewood–Richardson Coefficients

DK Nguyen - Annals of Combinatorics, 2022 - Springer
We give a new interpretation of the shifted Littlewood–Richardson coefficients f λ μ ν (λ, μ, ν
are strict partitions). The coefficients g λ μ which appear in the decomposition of Schur Q …

Queer supercrystal structure for increasing factorizations of fixed-point-free involution words

T Hiroshima - Journal of Algebraic Combinatorics, 2023 - Springer
We show that the set of increasing factorizations of fixed-point-free (FPF) involution words
has the structure of queer supercrystals. By exploiting the algorithm of symplectic shifted …

[图书][B] A trilogy of (super) crystals: the queer, the set-valued and the hook-valued

W Poh - 2021 - search.proquest.com
This dissertation compiles three main results concerning crystals or supercrystals. Firstly, we
present a characterization for queer supercrystals introduced by Grantcharov et al. We also …