Abstract
Recently, G. I. Ol’shanskii introduced a new class of semifinite factor representations and their associated matrix coefficients, called generalized characters, which include the essential features of finite character theory for the infinite dimensional classical groups. They are related to the concept of total positivity [Kar] which has important applications in analysis, combinatorics, and to the theory of operator nodes and their characteristic functions which were introduced to study non self-adjoint Hilbert space operators. In [04], Ol’shanskii classified generalized characters associated to the infinite symmetric groups. In this situation, they are related to the Brauer semigroups which, together with their q-analogues, have important applications in knot theory and in the study of the Yang-Baxter equation (see [04] for references). The association of all these ideas suggest that the investigation of generalized characters may provide new insight in these areas. In this paper, we use C*-algebraic methods developed in [Boy2] to begin the classification of certain generalized characters associated to the unitary group.
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Boyer, R.P. (1994). Generalized Characters of U∞. In: Curto, R.E., Jørgensen, P.E.T. (eds) Algebraic Methods in Operator Theory. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0255-4_23
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DOI: https://doi.org/10.1007/978-1-4612-0255-4_23
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