Gaudin Hamiltonians on unitarizable modules over classical Lie (super)algebras

Research output: Contribution to journalArticlepeer-review

Abstract

Let M be a tensor product of unitarizable irreducible highest weight modules over the Lie (super)algebra G, where G is gl(m|n), osp(2m|2n) or spo(2m|2n). We show, using super duality, that the singular eigenvectors of the (super) Gaudin Hamiltonians for G on M can be obtained from the singular eigenvectors of the Gaudin Hamiltonians for the corresponding Lie algebras on some tensor products of finite-dimensional irreducible modules. As a consequence, the (super) Gaudin Hamiltonians for G are diagonalizable on the space spanned by singular vectors of M and hence on M. In particular, we establish the diagonalization of the Gaudin Hamiltonians, associated to any of the orthogonal Lie algebra so(2n) and the symplectic Lie algebra sp(2n), on the tensor product of infinite-dimensional unitarizable irreducible highest weight modules.

Original languageEnglish
Pages (from-to)400-431
Number of pages32
JournalJournal of Algebra
Volume642
DOIs
Publication statusPublished - 2024 Mar 15

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Fingerprint

Dive into the research topics of 'Gaudin Hamiltonians on unitarizable modules over classical Lie (super)algebras'. Together they form a unique fingerprint.

Cite this