Generalized \(Q\)-functions and \(UC\) hierarchy of \(B\)-type
type: Item
instance of: scholarly article
title: Generalized \(Q\)-functions and \(UC\) hierarchy of \(B\)-type
zbMATH Open document ID: 1195.05080
author: Yuji Ogawa
published in: Tokyo Journal of Mathematics
publication date: 2010-07-09T00:00:00Z
review text: A generalization of the Schur \(Q\)-function is introduced. This generalization, called generalized \(Q\)-function, is indexed by any pair of strict partitions, and can be expressed by the Pfaffian. A connection to the theory of integrable systems is clarified. Firstly, the bilinear identities satisfied by the generalized \(Q\)-function are given and proved to be equivalent to a system of partial differential equations of infinite order. The system is called the \(UC\) hierarchy of \(B\)-type(\(BUC\) hierarchy). Secondly, the aigebraic structure of the \(BUC\) hierarchy is investigated from the representation theoretic viewpoint. Some new kind of the boson-fermion correspondence is established, and a representation of an infinite dimensional Lie algebra, denoted by \({\frac go}_{2\infty}\), is obtained. The bilinear identities are translated to the language of neutral fermions, which turn out to characterize a \(G\)-orbit of the vacuum vector, where \(G\) is the group corresponding to \({\frac go}_{2\infty}\).
reviewed by: Victor Sharapov
Mathematics Subject Classification ID: 05E05
Mathematics Subject Classification ID: 05E10
Mathematics Subject Classification ID: 17B80
Mathematics Subject Classification ID: 37Kxx
zbMATH DE Number: 5734868
zbMATH Keywords: Continuous flows
zbMATH Keywords: discrete flows
zbMATH Keywords: \(f\)-flows
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1264170236
OpenAlex ID: W2075015751
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DOI: 10.3836/TJM/1264170236
description: scientific article; zbMATH DE number 5734868