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Quivers with Involutions and Shifted Twisted Yangians via Coulomb Branches II

Zichang Wang

Abstract

To a quiver with involution, we show that there is an algebra homomorphism from the corresponding shifted twisted Yangian to the quantized Coulomb branch algebra of the 3d $\mathcal{N}=4$ involution-fixed part of the quiver gauge theory in the second symmetric power case.

Quivers with Involutions and Shifted Twisted Yangians via Coulomb Branches II

Abstract

To a quiver with involution, we show that there is an algebra homomorphism from the corresponding shifted twisted Yangian to the quantized Coulomb branch algebra of the 3d involution-fixed part of the quiver gauge theory in the second symmetric power case.
Paper Structure (21 sections, 15 theorems, 117 equations)

This paper contains 21 sections, 15 theorems, 117 equations.

Table of Contents

  1. Introduction
  2. Coulomb branches of cotangent type
  3. BFN Coulomb Branch
  4. Quiver with involution
  5. Monopole operators
  6. Shifted twisted Yangians
  7. Main Results
  8. Preparations for the proof of relations
  9. Notations
  10. Expressions of $(H_i(z))^\circ$
  11. Serre-type relations for $y_{i,r}$
  12. Relations
  13. Relation \ref{['eq:hbcomm']}: commutativity of $h_{i,r}$ and $b_{j,s}$
  14. Relation \ref{['eq:bcomm']}: commutativity of $b_{i,r}$'s
  15. The case $j\notin\{i,\tau i\}$
  16. ...and 6 more sections

Key Result

Theorem 1

There is an algebra homomorphism from the shifted twisted Yangians $\mathbf{Y}^{\tau}_{\mu}(\mathfrak{g})\otimes H_{G_W}^*(\mathsf{pt})$ to the quantized Coulomb branch algebra associated to

Theorems & Definitions (28)

  • Theorem : \ref{['thm:main']}
  • Remark 2.1
  • Example 2.2: Type AIII
  • Proposition 2.3
  • Proposition 2.4
  • Definition 3.1
  • Lemma 4.1
  • proof
  • Theorem 4.2
  • Remark 4.3
  • ...and 18 more