Highest weight crystals for Schur \(Q\)-functions

zbMath1515.05200arXiv2112.02848MaRDI QIDQ6103843

Eric Marberg, Kam Hung Tong

Publication date: 5 June 2023

Published in: Séminaire Lotharingien de Combinatoire (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2112.02848

zbMATH Keywords

Schur \(Q\)-functionsshifted tableauxcrystalsqueer Lie superalgebrasinvolution words

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Grassmannians, Schubert varieties, flag manifolds (14M15) Representations of Lie algebras and Lie superalgebras, analytic theory (17B15) Combinatorial aspects of groups and algebras (05E16) Combinatorial aspects of algebraic geometry (05E14)

Cites Work

• Crystal bases for the quantum queer superalgebra
• On crystal bases of the \(q\)-analogue of universal enveloping algebras
• Dual filtered graphs
• Balanced tableaux
• Bumping operators and insertion algorithms for queer supercrystals
• A symplectic refinement of shifted Hecke insertion
• Toward a local characterization of crystals for the quantum queer superalgebra
• \(\mathfrak{q}\)-crystal structure on primed tableaux and on signed unimodal factorizations of reduced words of type \(B\)
• Crystalizing the q-analogue of universal enveloping algebras
• Crystal bases for the quantum queer superalgebra and semistandard decomposition tableaux
• Crystal Bases
• Canonical Bases Arising from Quantized Enveloping Algebras
• Canonical Bases Arising from Quantized Enveloping Algebras. II
• Crystal Approach to Affine Schubert Calculus
• Crystal analysis of type \(C\) Stanley symmetric functions

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