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- Title
Vertex Operators Arising from Jacobi-Trudi Identities.
- Authors
Jing, Naihuan; Rozhkovskaya, Natasha
- Abstract
We give an interpretation of the boson-fermion correspondence as a direct consequence of the Jacobi-Trudi identity. This viewpoint enables us to construct from a generalized version of the Jacobi-Trudi identity the action of a Clifford algebra on the polynomial algebras that arrive as analogues of the algebra of symmetric functions. A generalized Giambelli identity is also proved to follow from that identity. As applications, we obtain explicit formulas for vertex operators corresponding to characters of the classical Lie algebras, shifted Schur functions, and generalized Schur symmetric functions associated to linear recurrence relations.
- Subjects
VERTEX operator algebras; JACOBI identity; INTERACTING boson-fermion models; SYMMETRIC functions; RECURSIVE sequences (Mathematics)
- Publication
Communications in Mathematical Physics, 2016, Vol 346, Issue 2, p679
- ISSN
0010-3616
- Publication type
Article
- DOI
10.1007/s00220-015-2564-9