Back to Search
Start Over
Chevalley formula for anti-dominant weights in the equivariant K-theory of semi-infinite flag manifolds.
- Source :
-
Advances in Mathematics . Aug2021, Vol. 387, pN.PAG-N.PAG. 1p. - Publication Year :
- 2021
-
Abstract
- We prove a Chevalley formula for anti-dominant weights in the torus-equivariant K -group of semi-infinite flag manifolds, which is described explicitly in terms of semi-infinite Lakshmibai-Seshadri paths (or equivalently, quantum Lakshmibai-Seshadri paths); in contrast to the Chevalley formula for dominant weights in our previous paper [17] , the formula for anti-dominant weights has a significant finiteness property. Based on geometric results established in [17] , our proof is representation-theoretic, and the Chevalley formula for anti-dominant weights follows from a certain identity for the graded characters of Demazure submodules of a level-zero extremal weight module over a quantum affine algebra; in the proof of this identity, we make use of the (combinatorial) standard monomial theory for semi-infinite Lakshmibai-Seshadri paths, and also a string property of Demazure-like subsets of the set of semi-infinite Lakshmibai-Seshadri paths of a fixed shape, which gives an explicit realization of the crystal basis of a level-zero extremal weight module. [ABSTRACT FROM AUTHOR]
- Subjects :
- *K-theory
*FINITE, The
*ALGEBRA
*CRYSTALS
*CALCULUS
*AFFINE algebraic groups
Subjects
Details
- Language :
- English
- ISSN :
- 00018708
- Volume :
- 387
- Database :
- Academic Search Index
- Journal :
- Advances in Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 151288922
- Full Text :
- https://doi.org/10.1016/j.aim.2021.107828