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Twisted Yangians and Steinberg varieties of type C

Changjian Su, Yang Yang

Abstract

We study the equivariant homology of the generalized Steinberg variety of type C and show that there exists a surjective algebra homomorphism from the twisted Yangian of type $\AIII_{2n}^{(τ)}$ to it.

Twisted Yangians and Steinberg varieties of type C

Abstract

We study the equivariant homology of the generalized Steinberg variety of type C and show that there exists a surjective algebra homomorphism from the twisted Yangian of type to it.

Paper Structure

This paper contains 30 sections, 23 theorems, 218 equations.

Table of Contents

  1. Introduction
  2. Convolutions and Steinberg varieties of type C
  3. Convolution in equivariant Borel--Moore homology
  4. Partial flag varieties of type C
  5. A pushforward formula
  6. The Steinberg variety
  7. A generating set for the convolution algebra
  8. The correspondences and operators
  9. The combinatorial operators
  10. The geometric $H$ operators
  11. The geometric $B$-operators
  12. Involution
  13. Main results
  14. Twisted Yangian
  15. The algebra homomorphism
  16. ...and 15 more sections

Key Result

Theorem 1.1

There exists an algebra homomorphism and it is surjective if we specialize to a semisimple element $(s,t)\in \mathfrak{g}\times \mathbb{C}$ with $t\neq 0$.

Theorems & Definitions (40)

  • Theorem 1.1: Theorem \ref{['thm:main']} and \ref{['surj']}
  • Lemma 2.1
  • Proposition 2.2
  • Proposition 2.3
  • Lemma 2.4
  • proof
  • Corollary 2.5
  • proof
  • Proposition 2.6
  • proof
  • ...and 30 more