Determining a semisimple group from its representation degrees
Michael J. Larsen
TL;DR
This paper explores how the degrees of irreducible representations can determine a compact semisimple Lie group's Lie algebra, highlighting limitations when different groups share the same representation degrees.
Contribution
It investigates the extent to which representation degrees uniquely identify the Lie algebra of a compact semisimple Lie group, revealing potential ambiguities.
Findings
Representation degrees determine the Lie algebra in many cases.
Different groups can have identical sets of representation degrees.
The paper clarifies conditions under which the group is uniquely identified.
Abstract
The Lie algbera of a compact semisimple Lie group G is determined by the degrees of the irreducible representations of G. However, two different groups can have the same representation degrees.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Advanced Topics in Algebra · Finite Group Theory Research