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Gaudin model and Deligne’s category.
- Source :
-
Letters in Mathematical Physics . Feb2024, Vol. 114 Issue 1, p1-43. 43p. - Publication Year :
- 2024
-
Abstract
- We show that the construction of the higher Gaudin Hamiltonians associated with the Lie algebra gl n admits an interpolation to any complex number n. We do this using the Deligne’s category D t , which is a formal way to define the category of finite-dimensional representations of the group G L n , when n is not necessarily a natural number. We also obtain interpolations to any complex number n of the no-monodromy conditions on a space of differential operators of order n, which are considered to be a modern form of the Bethe ansatz equations. We prove that the relations in the algebra of higher Gaudin Hamiltonians for complex n are generated by our interpolations of the no-monodromy conditions. Our constructions allow us to define what it means for a pseudo-differential operator to have no monodromy. Motivated by the Bethe ansatz conjecture for the Gaudin model associated with the Lie superalgebra gl n | n ′ , we show that a ratio of monodromy-free differential operators is a pseudo-differential operator without monodromy. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03779017
- Volume :
- 114
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Letters in Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 174455991
- Full Text :
- https://doi.org/10.1007/s11005-023-01747-y