We prove a Schur-Weyl duality between the quantum enveloping algebra of $\mathfrak{gl}_m$ and certain quotient algebras Ariki-Koike algebras, which we give explicitly. The involves several algebraically independent parameters is realized through tensor product parabolic universal Verma module power natural representation $\mathfrak{gl}_m$. also new presentation by generators relations generaliz...

We are concerned with the compatible gauge reformulation for H(div) equations and the design of fast solvers of the resulting linear algebraic systems as in [5]. We propose an algebraic reformulation of the discrete H(div) equations along with an algebraic multigrid (AMG) technique for the reformulated problem. The reformulation uses discrete Hodge decompositions on co-chains to replace the dis...

Abstract By an approximate subring of a ring we mean additively symmetric subset X such that $$X\cdot \cup (X +X)$$ X · ∪ ( + ) is covered by finitely many additive translates . We prove each has locall...

A classical construction associates to a transient random walk on discrete group $$\Gamma $$ compact -space $$\partial _M \Gamma known as the Martin boundary. The resulting crossed product $$C^*$$ -algebra $$C(\partial ) \rtimes _r comes equipped with one-parameter of automorphisms given by kernels that define In this paper we study KMS states for flow and obtain complete description when Poiss...

Abstract The purpose of this paper and its sequel is to develop the geometry built from commutative algebras that naturally appear as homology differential graded and, more generally, homotopy in spectra. question are those symmetric monoidal category abelian groups, being commutative, they form affine building blocks a geometry, rings algebraic geometry. We name Dirac because grading exhibits ...