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GKLO representations for shifted quantum affine symmetric pairs

Jian-Rong Li, Tomasz Przezdziecki

Abstract

In this note, we introduce shifted quantum affine symmetric pairs of split simply-laced type, and construct their GKLO representations, following similar recent developments in the case of shifted twisted Yangians. A full proof that our formulas yield a representation is given.

GKLO representations for shifted quantum affine symmetric pairs

Abstract

In this note, we introduce shifted quantum affine symmetric pairs of split simply-laced type, and construct their GKLO representations, following similar recent developments in the case of shifted twisted Yangians. A full proof that our formulas yield a representation is given.
Paper Structure (17 sections, 9 theorems, 92 equations)

This paper contains 17 sections, 9 theorems, 92 equations.

Table of Contents

  1. Introduction
  2. Shifted quantum affine symmetric pairs
  3. GKLO representations
  4. Algebra of difference operators
  5. Special operators
  6. GKLO homomorphism
  7. Proof: part I
  8. Auxiliary results
  9. Proof of the main theorem
  10. Relation \ref{['eq: drel2']}
  11. Relation \ref{['eq: drel4']}
  12. Relation \ref{['eq: drel5']}
  13. Proof: part II - Serre relations
  14. The LHS
  15. The vanishing coefficients
  16. ...and 2 more sections

Key Result

Lemma 3.4

We have for Hence

Theorems & Definitions (24)

  • Definition 2.1
  • Remark 3.1
  • Definition 3.2
  • Definition 3.3
  • Lemma 3.4
  • proof
  • Theorem 3.5
  • Remark 3.6
  • Remark 3.7
  • Remark 3.8
  • ...and 14 more