Demazure character formula for semi-infinite flag varieties

Abstract

We provide a proof that every Schubert variety of a semi-infinite flag variety is projectively normal. This gives us an interpretation of a Demazure module of a global Weyl module of a current Lie algebra as the (dual) space of the space of global sections of a semi-infinite Schubert variety. Moreover, we give geometric realizations of Feigin-Makedonskyi's generalized Weyl modules, and the $t=\infty$ specialization of non-symmetric Macdonald polynomials.

30pages, v3: corrected Corollary 5.2 and vanishing theorems in section 6, v4: title changed, many small changes, to appear in Math. Ann

References in corpus (1)

• A uniform model for Kirillov-Reshetikhin crystals III: Nonsymmetric Macdonald polynomials at $t=0$ and Demazure characters

Cited by in corpus (6)

• Equivariant $K$-theory of semi-infinite flag manifolds and Pieri-Chevalley formula
• Reduced arc schemes for Veronese embeddings and global Demazure modules
• Frobenius splitting of Schubert varieties of semi-infinite flag manifolds
• Vertex algebras and coordinate rings of semi-infinite flags
• Beilinson-Drinfeld Schubert varieties and global Demazure modules
• On reduced arc spaces of toric varieties