The representation theory of the affine Hecke algebras has two different approaches. One is a geometric approach and the other is a combinatorial one. In the equal parameter case, affine Hecke algebras are constructed using equivariant K-groups, and their irreducible representations are constructed on Borel-Moore homologies. By this method, their irreducible representations are parameterized by...

The relation between facets of Rees cones of clutters and irreducible b-vertex covers is examined. Let G be a simple graph and let Ic(G) be its ideal of vertex covers. We give a graph theoretical description of the irreducible bvertex covers of G, i.e., we describe the minimal generators of the symbolic Rees algebra of Ic(G). As an application we recover an explicit description of the edge cone...

The solution set V of a polynomial system, i.e., the set of common zeroes of a set of multivariate polynomials with complex coefficients, may contain several components, e.g., points, curves, surfaces, etc. Each component has attached to it a number of quantities, one of which is its dimension. Given a numerical approximation to a point p on the set V , this article presents an efficient algori...

A finite group $G$ is called rational if all its irreducible complex characters are rational valued. In this paper we discuss about rational groups with Sylow 2-subgroups of nilpotency class at most 2 by imposing the solvability and nonsolvability assumption on $G$ and also via nilpotency and nonnilpotency assumption of $G$.

‎In this note‎, ‎we consider the concentration function problem for a continuous action of a locally compact group $G$ on a locally compact Hausdorff space $X$‎. ‎We prove a necessary and sufficient condition for the concentration functions of a‎ ‎spread-out irreducible probability measure $mu$ on $G$ to converge to zero.

Let $f : A rightarrow B$ be a ring homomorphism and $J$ an ideal of $B$. In this paper, we give a necessary and sufficient condition for the amalgamated algebra along an ideal $Abowtie^fJ$ to be $J$-Noetherian. Then we give a characterization for pseudo-irreducible ideals of $Abowtie^fJ$, in special cases.

We show that if G is a graph such that every edge is in at least two triangles, then G contains a spanning tree with no vertex of degree 2 (a homeomorphically irreducible spanning tree). This result was originally asked in a question format by Albertson, Berman, Hutchinson, and Thomassen in 1979, and then conjectured to be true by Archdeacon in 2009. MSC2010 : 05C05, 05C75

We consider normalizers of an irreducible inclusion N ⊆ M of II1 factors. In the infinite index setting an inclusion uNu∗ ⊆ N can be strict, forcing us to also investigate the semigroup of one-sided normalizers. We relate these normalizers of N in M to projections in the basic construction and show that every trace one projection in the relative commutant N ′ ∩ 〈M, eN 〉 is of the form ueNu for ...