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Low-Dimensional Representations of Special Unitary Groups

✍ Scribed by Gerhard Hiss; Gunter Malle

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 170 KB
Volume: 236
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2000.8513

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✦ Synopsis

We prove gap results for the low-dimensional representation of unitary groups in nondefining characteristics. More precisely, we give a lower bound for the third smallest degree of a nontrivial absolutely irreducible representation of the groups mentioned above, which is almost in the order of magnitude of the square of the two smallest such representations. As a corollary we obtain the uniqueness of Weil representations in all cross characteristics for the unitary groups. Our approach uses some results on ordinary representations which can be proved using Deligne᎐Lusztig theory and which might be of independent interest, as well as information on decomposition matrices.

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