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表現論セミナー Crystals for set-valued decomposition tableaux（Eric MARBERG）

2023年12月05日

2023年12月13日開催

2023年12月13日 14時45分～ 2023年12月13日 16時15分

理学部3-210

Eric MARBERG氏 (香港科技大学(Hong Kong University of Science and Technology))

Crystals are certain directed acyclic graphs that generalize

the crystal bases of quantum group representations. The vertices in a

crystal often correspond to familiar combinatorial objects, and the

directed edges encode interesting operators on these objects. The

prototypical example is the crystal of semistandard tableaux of a fixed

shape. Monical, Pechenik, and Scrimshaw discovered a natural crystal

structure on semistandard set-valued tableaux, which arise in formulas

for K-theory representatives of type A Schubert varieties. This talk

will discuss a new “shifted” analogue of this crystal, whose vertices

are objects called set-valued decomposition tableaux. As one application,

the existence of this crystal implies a weaker form of a conjectural

formula for K-theoretic Schur P-functions due to Ikeda. This is joint

work with Tong Kam Hung.

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