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Parabolic presentations of the modular Super Yangian Y(M|N)

Hongmei Hu

Abstract

The present paper is devoted to extend parabolic presentations, depending on an arbitrary composition of M+N and an arbitrary 01-sequence, of the super Yangian Y(M|N) to a field of positive characteristic.

Parabolic presentations of the modular Super Yangian Y(M|N)

Abstract

The present paper is devoted to extend parabolic presentations, depending on an arbitrary composition of M+N and an arbitrary 01-sequence, of the super Yangian Y(M|N) to a field of positive characteristic.

Paper Structure

This paper contains 10 sections, 18 theorems, 189 equations.

Table of Contents

  1. Introduction
  2. Generalities on the Modular super Yangian $Y_{M|N}$
  3. $01$-sequence
  4. Restricted Lie superalgebra ${\mathfrak g\mathfrak l}_{M|N}[x]$
  5. Modular super Yangian $Y_{M|N}$
  6. Parabolic generators in positive characteristic
  7. Maps between Super Yangians
  8. Special Case: $n=2$
  9. Special Cases: $n=3$ and the super Serre relations
  10. The general case

Key Result

Proposition 2.2

Ordered supermonomial in the generators $\{t_{i,j}^{(r)};~1{\leq}i,j{\leq}M+N, r\geq 1\}$ taken in some fixed order forms a linear basis for $Y_{M|N}$.

Theorems & Definitions (30)

  • Definition 2.1
  • Proposition 2.2
  • Lemma 3.1
  • proof
  • Theorem 3.3
  • Proposition 4.1
  • proof
  • Proposition 4.2
  • Proposition 4.3
  • proof
  • ...and 20 more