Identities of Inverse Chevalley Type for the Graded Characters of Level-Zero Demazure Submodules over Quantum Affine Algebras of Type C

Abstract

AbstractWe provide identities of inverse Chevalley type for the graded characters of level-zero Demazure submodules of extremal weight modules over a quantum affine algebra of type C. These identities express the product $$e^{\mu } \text {gch} ~V_{x}^{-}(\lambda )$$ e μ gch V x - ( λ ) of the (one-dimensional) character $$e^{\mu }$$ e μ , where $$\mu $$ μ is a (not necessarily dominant) minuscule weight, with the graded character gch$$V_{x}^{-}(\lambda )$$ V x - ( λ ) of the level-zero Demazure submodule $$V_{x}^{-}(\lambda )$$ V x - ( λ ) over the quantum affine algebra $$U_{\textsf{q}}(\mathfrak {g}_{\textrm{af}})$$ U q ( g af ) as an explicit finite linear combination of the graded characters of level-zero Demazure submodules. These identities immediately imply the corresponding inverse Chevalley formulas for the torus-equivariant K-group of the semi-infinite flag manifold $$\textbf{Q}_{G}$$ Q G associated to a connected, simply-connected and simple algebraic group G of type C. Also, we derive cancellation-free identities from the identities above of inverse Chevalley type in the case that $$\mu $$ μ is a standard basis element $${\varepsilon }_{k}$$ ε k in the weight lattice P of G.