Introduced by Kawanaka in order to find the unipotent representations of finite groups of Lie type, generalized Gelfand–Graev characters have remained somewhat mysterious. Even in the case of the finite general linear groups, the combinatorics of their decompositions has not been worked out. This paper re-interprets Kawanaka’s definition in type A in a way that gives far more flexibility in com...

The Cauchy problem for systems of differential equations with multiplicative random perturbations in the form of infinitedimensional Ito integrals is studied. For the systems correct by Petrovskii, conditionally correct and incorrect we point out Gelfand–Shilov spaces of generalized functions where a generalized solution coincides with a mild solution. AMS Mathematics Subject Classification (20...

Mutations on Brauer configurations are introduced and associated with some suitable automata to solve generalizations of the Chicken McNugget problem. Additionally, based marked order polytopes, new Diophantine equations called Gelfand–Tsetlin also solved. The approach allows algebraic descriptions properties AES key schedule via configuration algebras non-deterministic finite (NFA).

We construct a new family of simple modules over orthogonal complex Lie algebra associated with Gelfand-Zetlin formulae for simple nite dimensional modules and study the corresponding Gelfand-Zetlin subalgebra.

Inspired by the results of [APR], we propose combinatorial Gelfand models for semigroup algebras of some finite semigroups, which include the symmetric inverse semigroup, the dual symmetric inverse semigroup, the maximal factorizable subsemigroup in the dual symmetric inverse semigroup, and the factor power of the symmetric group. Furthermore we extend the Gelfand model for the semigroup algebr...

Anti-normal quantization of relativistic Yang-Mills fields with a compact semisimple gauge group mathematically produces an infinite discrete energymass spectrum of Z′ gauge bosons. In particular, quantum Yang-Mills theory existence and mass gap problem is solved. To I. M. Gelfand with gratitude.