Pfaffian-type Sugawara operators

2011/07/27 by Alexander Molev, A. I. Molev, Molev, A. I.
Computer Science · Mathematics · Physics and Astronomy · #Advanced Algebra and Logic #Approximation Theory and Sequence Spaces #FOS: Mathematics #FOS: Physical sciences #Holomorphic and Operator Theory #Mathematical Physics (math-ph) #Representation Theory (math.RT) #math-ph #math.MP #math.RT

paper · pdf · doi:10.48550/arxiv.1107.5417

4 pages

arxiv created 2011/07/27 · openalex publication_date 2011/07/27 · arxiv updated 2012/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the Pfaffian of a generator matrix for the affine Kac--Moody algebra hat o_2n is a Segal--Sugawara vector. Together with our earlier construction involving the symmetrizer in the Brauer algebra, this gives a complete set of Segal--Sugawara vectors in type D.

Citations

• Quantum spectral curves, quantum integrable systems and the geometric Langlands correspondence

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• Geometric Realization of the Segal--Sugawara Construction