For each integer t > 0 and each simple Lie algebra g, we determine the least dimension of an irreducible highest weight representation of g whose highest weight has width t. As a consequence, we classify all irreducible modules whose dimension equals a product of two primes. This consequence, which was in fact the driving force behind our paper, answers a question of N. Katz.

The irreducible supersingular mod p representations of G = GL2(F ), where F is a finite extension of Qp, are the building blocks of the mod p representation theory of G. They all arise as irreducible quotients of certain universal supersingular representations. We investigate the structure of these universal modules in the case when F/Qp is totally ramified.

We describe irreducible conformal subalgebras of CendN and build the structure theory of associative conformal algebras with finite faithful representation.

Let F be a locally compact non-Archimedean field, and let B/F be a division algebra of dimension 4. The JacquetLanglands correspondence provides a bijection between smooth irreducible representations π′ of B× of dimension > 1 and irreducible cuspidal representations of GL2(F ). We present a new construction of this bijection in which the preservation of epsilon factors is automatic. This is don...

We investigate the question when the tensor square, the alternating square, or the symmetric square of an absolutely irreducible projective representation V of an almost simple group G is again irreducible. The knowledge of such representations is of importance in the description of the maximal subgroups of simple classical groups of Lie type. We show that if G is of Lie type in odd characteris...

Consider the field F2n . Its elements are presented as polynomials from F2[x] modulo some irreducible polynomial of degree n. This polynomial can be found in time polynomial in n, as well as the matrix that related two representation corresponding to different irreducible polynomials [2]. Therefore, we do not need to specify a choice of the irreducible polynomial speaking about polynomial reduc...

An SO(4) gauge invariant model with extended field transformations is examined in four dimensional Euclidean space. The gauge field is (A µ) αβ = 1 2 t µνλ (M νλ) αβ where M νλ are the SO(4) generators in the fundamental representation. The SO(4) gauge indices also participate in the Euclidean space SO(4) transformations giving the extended field transformations. We provide the decomposition of...