2020/08/24 by Takafumi Kouno, Satoshi Naito, Kouno, Takafumi +5
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Geometry and complex manifolds #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2008.10483
openalex publication_date 2020/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove an explicit inverse Chevalley formula in the equivariant K-theory\nof semi-infinite flag manifolds of simply-laced type. By an inverse Chevalley\nformula, we mean a formula for the product of an equivariant scalar with a\nSchubert class, expressed as a \ℤ[q\± 1]-linear combination of\nSchubert classes twisted by equivariant line bundles. Our formula applies to\narbitrary Schubert classes in semi-infinite flag manifolds of simply-laced type\nand equivariant scalars e\λ, where \λ is an arbitrary\nminuscule weight. By a result of Stembridge, our formula completely determines\nthe inverse Chevalley formula for arbitrary weights in simply-laced type,\nexcept for type E8. The combinatorics of our formula is governed by the\nquantum Bruhat graph, and the proof is based on a limit from the double affine\nHecke algebra. As such, our formula also provides an explicit determination of\nall nonsymmetric q-Toda operators for minuscule weights in ADE type.\n