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On the Depth of the Invariants of the Symmetric Power Representations of SL2(Fp)

✍ Scribed by R.James Shank; David L. Wehlau

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 99 KB
Volume: 218
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.7878

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✦ Synopsis

We study the depth of the ring of invariants of SL F acting on the nth 2 p symmetric power of the natural two-dimensional representation for np. These Ž . symmetric power representations are the irreducible representations of SL F 2 p over F . We prove that, when the greatest common divisor of p y 1 and n is less p than or equal to 2, the depth of the ring of invariants is 3. We also prove that the depth is 3 for n s 3, p / 7 and n s 4, p / 5. However, for n s 3, p s 7 the depth is 4 and for n s 4, p s 5 the depth is 5. In these two exceptional cases, the ring of invariants is Cohen᎐Macaulay.

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