Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A large deviation principle for the reduction of product representations

Author: N. G. Duffield
Journal: Proc. Amer. Math. Soc. 109 (1990), 503-515
MSC: Primary 60B15; Secondary 22C05, 60J15
MathSciNet review: 1004418
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A large deviation principle is proved for a family of measures $ \left\{ {{\mathbb{L}_n}:n = 1,2, \ldots } \right\}$ derived from the multiplicities occurring in the decomposition into irreducible components of $ n$-fold tensor products of representations of arbitrary compact semisimple Lie groups.

References [Enhancements On Off] (What's this?)

  • [1] W. Cegła, J. T. Lewis, and G. A. Raggio, The free energy of quantum spin systems and large deviations, Comm. Math. Phys. 118 (1988), no. 2, 337–354. MR 956171
  • [2] S. R. S. Varadhan, Asymptotic probabilities and differential equations, Comm. Pure Appl. Math. 19 (1966), 261–286. MR 0203230
  • [3] Richard S. Ellis, Entropy, large deviations, and statistical mechanics, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 271, Springer-Verlag, New York, 1985. MR 793553
  • [4] N. G. Duffield, Classical and thermodynamic limits for generalised quantum spin systems, Comm. Math. Phys. 127 (1990), no. 1, 27–39. MR 1036113
  • [5] D. Petz, G. A. Raggio, and A. Verbeure, Asymptotics of Varadhan-type and the Gibbs variational principle, Comm. Math. Phys. 121 (1989), no. 2, 271–282. MR 985399
  • [6] G. A. Raggio and R. F. Werner, Quantum statistical mechanics of general mean field systems, Helv. Phys. Acta 62 (1989), no. 8, 980–1003. MR 1034151
  • [7] Hans Samelson, Notes on Lie algebras, Van Nostrand Reinhold Mathematical Studies, No. 23, Van Nostrand Reinhold Co., New York- London-Melbourne, 1969. MR 0254112
  • [8] Anthony W. Knapp, Representation theory of semisimple groups, Princeton Mathematical Series, vol. 36, Princeton University Press, Princeton, NJ, 1986. An overview based on examples. MR 855239

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 60B15, 22C05, 60J15

Retrieve articles in all journals with MSC: 60B15, 22C05, 60J15

Additional Information

Keywords: Large deviations, Lie groups, reduction of representations
Article copyright: © Copyright 1990 American Mathematical Society