On some properties of symplectic Grothendieck polynomials
| Autor: | Eric Marberg, Brendan Pawlowski |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Symplectic group Flag (linear algebra) 010102 general mathematics Limiting 01 natural sciences Mathematics::Algebraic Geometry Grassmannian 0103 physical sciences FOS: Mathematics Mathematics - Combinatorics 010307 mathematical physics Combinatorics (math.CO) 0101 mathematics Orbit (control theory) Variety (universal algebra) Representation Theory (math.RT) Mathematics::Representation Theory Mathematics::Symplectic Geometry Mathematics - Representation Theory Symplectic geometry Mathematics |
| Popis: | Grothendieck polynomials, introduced by Lascoux and Sch\"utzenberger, are certain $K$-theory representatives for Schubert varieties. Symplectic Grothendieck polynomials, described more recently by Wyser and Yong, represent the $K$-theory classes of orbit closures for the complex symplectic group acting on the complete flag variety. We prove a transition formula for symplectic Grothendieck polynomials and study their stable limits. We show that each of the $K$-theoretic Schur $P$-functions of Ikeda and Naruse arises from a limiting procedure applied to symplectic Grothendieck polynomials representing certain "Grassmannian" orbit closures. Comment: 24 pages; v2: minor edits, updated references, final version |
| Databáze: | OpenAIRE |
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