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Certain partial orders on semigroups

Mario Petrich (2001)

Czechoslovak Mathematical Journal

Relations introduced by Conrad, Drazin, Hartwig, Mitsch and Nambooripad are discussed on general, regular, completely semisimple and completely regular semigroups. Special properties of these relations as well as possible coincidence of some of them are investigated in some detail. The properties considered are mainly those of being a partial order or compatibility with multiplication. Coincidences of some of these relations are studied mainly on regular and completely regular semigroups.

Character formulae for classical groups

Péter Frenkel (2006)

Open Mathematics

We give formulae relating the value Xλ (g) of an irreducible character of a classical group G to entries of powers of the matrix g ε G. This yields a far-reaching generalization of a result of J.L. Cisneros-Molina concerning the GL 2 case [1].

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