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A Drinfeld-type presentation of the orthosymplectic Yangians

A. I. Molev

Abstract

We use the Gauss decomposition of the generator matrix in the $R$-matrix presentation of the Yangian for the orthosymplectic Lie superalgebra ${\frak osp}_{N|2m}$ to produce its Drinfeld-type presentation. The results rely on a super-version of the embedding theorem which allows one to identify a subalgebra in the $R$-matrix presentation which is isomorphic to the Yangian associated with ${\frak osp}_{N|2m-2}$.

A Drinfeld-type presentation of the orthosymplectic Yangians

Abstract

We use the Gauss decomposition of the generator matrix in the -matrix presentation of the Yangian for the orthosymplectic Lie superalgebra to produce its Drinfeld-type presentation. The results rely on a super-version of the embedding theorem which allows one to identify a subalgebra in the -matrix presentation which is isomorphic to the Yangian associated with .
Paper Structure (7 sections, 11 theorems, 170 equations)

This paper contains 7 sections, 11 theorems, 170 equations.

Table of Contents

  1. Introduction
  2. Basic properties of the orthosymplectic Yangian
  3. The embedding theorem
  4. Gaussian generators
  5. Multiplicative formula for $c(u)$
  6. Drinfeld presentation of the extended Yangian
  7. Proof of the Main Theorem

Key Result

Theorem 3.1

For $m\geqslant 1$ the mapping defines an injective homomorphism ${\rm X}(\mathfrak{osp}_{N|2m-2})\to {\rm X}(\mathfrak{osp}_{N|2m})$. Moreover, its restriction to the subalgebra ${\rm Y}(\mathfrak{osp}_{N|2m-2})$ defines an injective homomorphism ${\rm Y}(\mathfrak{osp}_{N|2m-2})\to {\rm Y}(\mathfrak{osp}_{N|2m})$.

Theorems & Definitions (18)

  • Theorem 3.1
  • proof
  • Corollary 3.2
  • Corollary 3.3
  • Lemma 4.1
  • proof
  • Proposition 4.2
  • Lemma 4.3
  • proof
  • Proposition 5.1
  • ...and 8 more