Schubert varieties and the fusion products

2003/05/30 by Boris Feigin, B. Feigin, Evgeny Feigin +3
Mathematics · #17B67 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:17B67

paper · pdf · doi:10.48550/arxiv.math/0305437

34 pages

openalex publication_date 2003/05/30 · arxiv created 2004/02/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For each A∈\Nⁿ we define a Schubert variety \sh_A as a closure of the \Slt(\C[t])-orbit in the projectivization of the fusion product M^A. We clarify the connection of the geometry of the Schubert varieties with an algebraic structure of M^A as \slt⊗\C[t] modules. In the case when all the entries of A are different \sh_A is smooth projective algebraic variety. We study its geometric properties: the Lie algebra of the vector fields, the coordinate ring, the cohomologies of the line bundles. We also prove, that the fusion products can be realized as the dual spaces of the sections of these bundles.

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