Decomposing Monomial Representations of Solvable Groups

Good Representations and Solvable Groups

The purpose of this paper is to provide a characterization of solvable linear algebraic groups in terms of a geometric property of representations. Representations with a related property played an important role in the proof of the equivariant Riemann-Roch theorem [EG2]. In that paper, we constructed representations with that property (which we call freely good) for the group of upper triangul...

Decomposing permutation representations of symmetric groups

Quantization and Representations of Solvable Lie Groups

Introduction. In this note, we will announce a characterization of a connected, simply connected Type I solvable Lie group, G, and present a complete description of the set of all unitary equivalence classes of irreducible unitary representations of G together with a construction of an irreducible representation in each equivalence class. This result subsumes the results previously obtained on ...

Decomposing Symmetric Powers of Certain Modular Representations of Cyclic Groups

For a prime number p, we construct a generating set for the ring of invariants for the p+1 dimensional indecomposable modular representation of a cyclic group of order p. We then use the constructed invariants to describe the decomposition of the symmetric algebra as a module over the group ring, confirming the Periodicity Conjecture of Ian Hughes and Gregor Kemper for this case.

Decomposing Representations of Finite Groups on Riemann-roch Spaces

If G is a finite subgroup of the automorphism group of a projective curve X and D is a divisor on X stabilized by G, then we compute a simplified formula for the trace of the natural representation of G on the Riemann-Roch space L(D), under the assumption that L(D) is “rational”, D is nonspecial, and the characteristic is “good”. We discuss the partial formulas that result if L(D) is not rational.