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VOL. 55 | 2009 Generalized Q-functions and UC hierarchy of B-type
Yuji Ogawa

Editor(s) Jean-Pierre Bourguignon, Motoko Kotani, Yoshiaki Maeda, Nobuyuki Tose


We define a generalization of Schur's Q-function for an arbitrary pair of strict partitions, which is called the generalized Q-function. We prove that all the generalized Q-functions solve a series of non-linear differential equations called the UC hierarchy of B-type (BUC hierarchy). We furthermore investigate the BUC hierarchy from the viewpoint of representation theory. We consider the Fock representation of the algebra of neutral fermions and establish the boson-fermion correspondence. Using this, we discuss the relationship between the BUC hierarchy and a certain infinite dimensional Lie algebra.


Published: 1 January 2009
First available in Project Euclid: 28 November 2018

zbMATH: 1196.17012
MathSciNet: MR2463507

Digital Object Identifier: 10.2969/aspm/05510309

Rights: Copyright © 2009 Mathematical Society of Japan


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