The totality of 4X4 matrices with coefficients in GF [22], determinant unity, and which permute among themselves the vectors of dimension 4 having 4 co-ordinates nonzero marks of GF [22], or 2 zeros and 2 nonzero marks of the field, forms a simple [l, p. 285, problem 9, part (4)]1 (multiplicative) group, G, of order 26-34-5. It will be demonstrated that G is isomorphic with no multiply transiti...

NC algorithms are given for determining the number and degrees of the factors, irreducible over the complex numbers C, of a multivariate polynomial with rational coeÆcients and for approximating each irreducible factor. NC is the class of functions computable by logspace-uniform boolean circuits of polynomial size and polylogarithmic depth. The measures of size of the input polynomial are its d...

I present several applications of the Dirac inequality to determination isolated unitary representations and associated “spectral gaps” in case unramified principal series. The method works particularly well order attach irreducible large nilpotent orbits (e.g., regular, subregular) Langlands dual complex Lie algebra. results could be viewed as a p-adic analogue Salamanca-Riba’s classification ...

Using vertex operators, we construct explicitly Lusztig’s Z[q, q−1]-lattice for the level one irreducible representations of quantum affine algebras of ADE type. We then realize the level one irreducible modules at roots of unity and show that the character is given by the Weyl-Kac character formula. 0. Introduction In [L1] and [L3] G. Lusztig proved that a quantum Kac-Moody algebra U defined o...

We establish a Kazhdan-Lusztig algorithm to compute characters of irreducible genuine representations of the (nonlinear) metaplectic group with half-integral infinitesimal character. We then prove a character multiplicity duality theorem for representations of Mp(2n,R) at fixed half-integral infinitesimal character. This allows us to extend some of Langlands’ ideas to Mp(2n,R).

For K/F a quadratic extension of p-adic fields, let σ be the conjugation relative to this extension, and ηK/F be the character of F ∗ with kernel norms of K. If π is a smooth irreducible representation of GL(n,K), and χ a character of F , the dimension of the space of linear forms on its space, which transform by χ under GL(n, F ) (with respect to the action [(L, g) 7→ L ◦ π(g)]) , is known to ...