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Explicit evaluation of the Stokes matrices for certain quantum confluent hypergeometric equations

Jinghong Lin, Xiaomeng Xu

Abstract

In this paper, we compute the Stokes matrices of a special quantum confluent hypergeometric system with Poincaré rank one. The sources of the interests in the Stokes phenomenon of such system are from representation theory and the theory of isomonodromy deformation.

Explicit evaluation of the Stokes matrices for certain quantum confluent hypergeometric equations

Abstract

In this paper, we compute the Stokes matrices of a special quantum confluent hypergeometric system with Poincaré rank one. The sources of the interests in the Stokes phenomenon of such system are from representation theory and the theory of isomonodromy deformation.
Paper Structure (13 sections, 27 theorems, 188 equations)

This paper contains 13 sections, 27 theorems, 188 equations.

Table of Contents

  1. Introduction
  2. Stokes matrices of a special (classical) confluent hypergeometric system
  3. Stokes matrices
  4. Diagonalization of the upper left submatrix of $A$
  5. Solutions of \ref{['classical new equation']} and its Stokes matrices
  6. Extension to all nonresonant $A$
  7. The explicit expression of Stokes matrices of quantum equation d
  8. The Stokes matrices of quantum equation \ref{['introqeq']}
  9. Quantum minors and Gelfand-Tsetlin basis
  10. Projection operator $\mathrm{Pr}_{i}$
  11. Diagonalization of the upper left submatrix of $T$
  12. Solutions of the equation \ref{['qn-1sys']} and its quantum Stokes matrices
  13. Extension of the Stokes matrices of quantum system \ref{['introqeq']}

Key Result

Theorem 1.1

The Stokes matrix $S_{h +}\left(E_{n},T\right)$ of the system introqeq takes the block matrix form where $b_{h+}=\left(\left(b_{h+}\right)_1,...,\left(b_{h+}\right)_{n-1}\right)^{\intercal}$ with entries as follows Here the elements $\ell^{\left(n-1\right)}_i\in \mathrm{End}\left(L\left(\lambda\right)\right)$, $\mathrm{Pr}_{i}\in {\rm End}\left(L\left(\lambda\right)\right)\otimes{\rm End}\left(\

Theorems & Definitions (57)

  • Theorem 1.1
  • Proposition 2.1
  • Definition 2.2
  • Definition 2.3
  • Proposition 2.4
  • Definition 2.5
  • Remark 2.6
  • Proposition 2.7
  • Lemma 2.8
  • proof
  • ...and 47 more