We classify all multiplicity-free products of Weyl characters, or equivalently, all multiplicity-free tensor products of irreducible representations of complex semisimple Lie algebras. As a corollary, we also obtain the classification of all multiplicity-free restrictions of irreducible representations to reductive subalgebras of parabolic type.

Let G be a finite group of order divisible by prime p . The number conjugacy classes -elements and -regular elements is at least 2 ? 1 Also, the -rational ? irreducible characters Along way we prove uniform lower bound for in simple Lie type terms its rank size underlying field.

Iwahori-Hecke algebras for the innnite series of complex reeection groups G(r; p; n) were constructed recently in the work of Ariki and Koike, Brou e and Malle, and Ariki. In this paper we give Murnaghan-Nakayama type formulas for computing the irreducible characters of these algebras. Our method is a generalization of that in our earlier paper in which we derived Murnaghan-Nakayama rules for t...

Given natural numbers m and n, we define a deflation map from the characters of the symmetric group Smn to the characters of Sn. This map is defined by first restricting a character of Smn to the wreath product Sm oSn, and then taking the sum of the irreducible constituents of the restricted character on which the base group Sm × · · · × Sm acts trivially. We prove a combinatorial formula which...

For finite Lie algebras, it is shown that characters can be defined first for Weyl orbits and then for irreducible representations. For AN Lie algebras, weight multiplicities can then be calculated by only stating that characters are equivalent to Schur functions. This also means that to calculate characters there is no need to sum over Weyl groups. The compatibility with the Weyl character for...

Abstract We give a description of the irreducible constituents restriction to Sylow 2-subgroups characters symmetric groups labelled by hook partitions.