Invariant and extendible group characters

Hecke Characters and Formal Group Characters

Let E be an elliptic curve over Q with complex multiplication by the ring of integers of an imaginary quadratic eld. Let be the Hecke character associated to E by the theory of complex multiplication. Let be the complex conjugate character of. For a pair of integers k and j, deene the Hecke character ' = '(k; j) = k j. Let p be a prime where E has good, ordinary reduction. Let p be a xed prime ...

Characters and Inversions in the Symmetric Group

We consider sums of the form π∈Sn χ λ/µ (π) q inv(π) where χ λ/µ is a skew character of the symmetric group and inv(π) is the number of inversions of π. Our main result gives a lower bound on the number of factors of 1 + q and 1 − q which divide the above sum, and is shown to be sharp when λ/µ is a hook partition shape. Résumé Nous considérons des sommes de la forme

Translation invariant surfaces in the 3-dimensional Heisenberg‎ ‎group

‎In this paper‎, ‎we study translation invariant surfaces in the‎ ‎3-dimensional Heisenberg group $rm Nil_3$‎. ‎In particular‎, ‎we‎ ‎completely classify translation invariant surfaces in $rm Nil_3$‎ ‎whose position vector $x$ satisfies the equation $Delta x = Ax$‎, ‎where $Delta$ is the Laplacian operator of the surface and $A$‎ ‎is a $3 times 3$-real matrix‎.

Double Coset Matrices and Group Characters

Group characters, permutation actions and sharpness

We extend the work which has appeared in papers on sharp characters and originated with Blichfeldt and Maillet to the Burnside ring of a finite group G. We show that the polynomial whose zeros are the set of marks of non-identity subgroups on a faithful G-set X evaluated at X is an integral multiple of the regular G-set, and deduce a result about the size of a base of X . Further consequences f...