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Borel-type presentation of the torus-equivariant quantum $K$-ring of flag manifolds of type $C$

Takafumi Kouno, Satoshi Naito

Abstract

We give a Borel-type presentation of the torus-equivariant (small) quantum $K$-ring of flag manifolds of type $C$.

Borel-type presentation of the torus-equivariant quantum $K$-ring of flag manifolds of type $C$

Abstract

We give a Borel-type presentation of the torus-equivariant (small) quantum -ring of flag manifolds of type .

Paper Structure

This paper contains 20 sections, 35 theorems, 137 equations, 2 tables.

Table of Contents

  1. Introduction
  2. Basic setting
  3. Notation for root systems
  4. The root system of type Cn
  5. The quantum K-ring of flag manifolds
  6. Borel-type presentation of QKT(G/B)
  7. Equivariant K-groups of semi-infinite flag manifolds
  8. Semi-infinite flag manifolds and the quantum K-ring
  9. Inverse Chevalley formula in type C
  10. Demazure operators
  11. Key relations in KT(QG)
  12. "Base" relation
  13. The other relations
  14. The solution to the recurrence relations
  15. Borel-type presentation
  16. ...and 5 more sections

Key Result

Theorem A

There exists an $R(T)[\![ Q ]\!]$-algebra isomorphism where $R(T)[\![ Q ]\!] := R(T)[\![ Q_{1}. \ldots, Q_{n} ]\!]$.

Theorems & Definitions (66)

  • Theorem A: = Theorem \ref{['thm:main']}
  • Definition 3.1
  • Example 3.2
  • Definition 3.3
  • Remark 3.4
  • Definition 3.5
  • Theorem 3.6
  • Theorem 4.1: Kato
  • Proposition 4.2: MNS
  • Theorem 4.3
  • ...and 56 more