Advanced Studies in Pure Mathematics

Generalized Q-functions and UC hierarchy of B-type

Yuji Ogawa

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Abstract

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.

Article information

Source
Noncommutativity and Singularities: Proceedings of French–Japanese symposia held at IHÉS in 2006, J.-P. Bourguignon, M. Kotani, Y. Maeda and N. Tose, eds. (Tokyo: Mathematical Society of Japan, 2009), 309-319

Dates
Received: 8 February 2007
Revised: 14 July 2008
First available in Project Euclid: 28 November 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1543447918

Digital Object Identifier
doi:10.2969/aspm/05510309

Mathematical Reviews number (MathSciNet)
MR2463507

Zentralblatt MATH identifier
1196.17012

Keywords
Schur's Q-functions BKP hierarchy universal characters UC hierarchy

Citation

Ogawa, Yuji. Generalized Q-functions and UC hierarchy of B-type. Noncommutativity and Singularities: Proceedings of French–Japanese symposia held at IHÉS in 2006, 309--319, Mathematical Society of Japan, Tokyo, Japan, 2009. doi:10.2969/aspm/05510309. https://projecteuclid.org/euclid.aspm/1543447918


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