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The size of infinite-dimensional representations

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Japanese Journal of Mathematics Aims and scope

Abstract

An infinite-dimensional representation π of a real reductive Lie group G can often be thought of as a function space on some manifold X. Although X is not uniquely defined by π, there are “geometric invariants” of π, first introduced by Roger Howe in the 1970s, related to the geometry of X. These invariants are easy to define but difficult to compute. I will describe some of the invariants, and recent progress toward computing them.

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Authors and Affiliations

  1. 2-355, Department of Mathematics, MIT, Cambridge, MA, 02139, USA

    David A. Vogan Jr.

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  1. David A. Vogan Jr.
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Correspondence to David A. Vogan Jr..

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Communicated by: Toshiyuki Kobayashi

This paper is offered in honor and in fond remembrance of Professor Bertram Kostant

This article is based on the 18th Takagi Lectures that the author delivered at the University of Tokyo on November 5–6, 2016.

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Vogan, D.A. The size of infinite-dimensional representations. Jpn. J. Math. 12, 175–210 (2017). https://doi.org/10.1007/s11537-017-1648-z

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  • DOI: https://doi.org/10.1007/s11537-017-1648-z

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