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

Event Date: Dec 13, 2023


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




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.