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Solutions to graded reflection equation of GL-type

D. Algethami, A. Mudrov, V. Stukopin

Abstract

We list solutions of the graded reflection equation associated with the fundamental vector representation of the quantum supergroup of GL-type.

Solutions to graded reflection equation of GL-type

Abstract

We list solutions of the graded reflection equation associated with the fundamental vector representation of the quantum supergroup of GL-type.
Paper Structure (5 sections, 10 theorems, 34 equations)

This paper contains 5 sections, 10 theorems, 34 equations.

Table of Contents

  1. Introduction
  2. $\mathbb{Z}_2$-graded Yang-Baxter and Reflection equations
  3. Classification of solutions
  4. Proof of the classification theorem
  5. Baxterization

Key Result

Proposition 2.1

The graded RE on $A\in \mathrm{End}(V)$ is equivalent to the non-graded RE with $\hat{S}^{ij}_{kl}=\breve S^{ij}_{kl}(-1)^{[i][j]+[k][l]}$, and $\hat{S}^{ij}_{kl}=\breve S^{ij}_{kl}$ under the assumption that $A$ is even.

Theorems & Definitions (21)

  • Proposition 2.1
  • proof
  • Definition 3.1
  • Theorem 3.2
  • Lemma 4.1
  • proof
  • Lemma 4.2
  • proof
  • Lemma 4.3
  • proof
  • ...and 11 more