On the Depth of the Invariants of the Symmetric Power Representations of SL2(Fp)
- Shank, R.James
- Wehlau, David L.
DOIAbstract
AbstractWe study the depth of the ring of invariants of SL2(Fp) acting on the nth symmetric power of the natural two-dimensional representation for n<p. These symmetric power representations are the irreducible representations of SL2(Fp) over Fp. We prove that, when the greatest common divisor of p−1 and n is less than or equal to 2, the depth of the ring of invariants is 3. We also prove that the depth is 3 for n=3, p≠7 and n=4, p≠5. However, for n=3, p=7 the depth is 4 and for n=4, p=5 the depth is 5. In these two exceptional cases, the ring of invariants is Cohen–Macaulay
Add to ORKG