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

We 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^μgch V_x^-(λ ) of the (one-dimensional) character e^μ , where μ is a (not necessarily dominant) minuscule weight, with the graded character gch V_x^-(λ ) of the level-zero Demazure submodule V_x^-(λ ) over the quantum affine algebra U_(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 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 μ is a standard basis element ε_k in the weight lattice P of G .