无限维表示的大小

IF 1.8 3区数学 Q1 MATHEMATICS

Japanese Journal of Mathematics Pub Date : 2017-08-21 DOI:10.1007/s11537-017-1648-z

David A. Vogan

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引用次数: 2

摘要

实约李群G的无限维表示π通常可以被认为是流形X上的函数空间。虽然X不是由π唯一定义的，但π有“几何不变量”，最早是由Roger Howe在20世纪70年代引入的，与X的几何有关。这些不变量很容易定义，但很难计算。我将描述一些不变量，以及计算它们的最新进展。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The size of infinite-dimensional representations

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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来源期刊

Japanese Journal of Mathematics 数学-数学

CiteScore

3.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The official journal of the Mathematical Society of Japan, the Japanese Journal of Mathematics is devoted to authoritative research survey articles that will promote future progress in mathematics. It encourages advanced and clear expositions, giving new insights on topics of current interest from broad perspectives and/or reviewing all major developments in an important area over many years. An eminent international mathematics journal, the Japanese Journal of Mathematics has been published since 1924. It is an ideal resource for a wide range of mathematicians extending beyond a small circle of specialists. The official journal of the Mathematical Society of Japan. Devoted to authoritative research survey articles that will promote future progress in mathematics. Gives new insight on topics of current interest from broad perspectives and/or reviews all major developments in an important area over many years.