We explicitly evaluate the generating functions for joint distributions of pairs of the permutation statistics inv, maj and ch over the symmetric group when both variables are set to −1. We give a combinatorial proof by means of a sign-reversing involution that specializing the variables to −1 in these bimahonian generating functions gives the number of two-colored permutations up to sign.

An S3-involution graph for a group G is a graph with vertex set a union of conjugacy classes of involutions of G such that two involutions are adjacent if they generate an S3-subgroup in a particular set of conjugacy classes. We investigate such graphs in general and also for the case where G = PSL(2, q).

An S3-involution graph for a group G is a graph with vertex set a union of conjugacy classes of involutions of G such that two involutions are adjacent if they generate an S3-subgroup in a particular set of conjugacy classes. We investigate such graphs in general and also for the case where G = PSL(2, q). 2000 Mathematics subject classification: 20B25, 05C25.

For a compact simply connected simple Lie group G with an involution α, we compute theGoZ/2-equivariant K-theory of G where G acts by conjugation and Z/2 acts either by α or by g 7→ α(g)−1. We also give a representation-theoretic interpretation of those groups, as well as of KG(G).

In this paper, we use the Drazin inverse to derive some new equivalences of the reverse order law for the group inverse in unitary rings. Moreover, if the ring has an involution, we present more equivalences when both involved elements are EP.

In this paper we construct a tilting sheaf for SeveriBrauer Varieties and Involution Varieties. This sheaf relates the derived category of each variety to the derived category of modules over a ring whose semisimple component consists of the Tits algebras of the corresponding linear algebraic group.

The goal of the article is to prove that four explicitly given transformations, two Heisenberg translations, a rotation and an involution generate the Picard modular group with Gaussian integers acting on the two dimensional complex hyperbolic space. The result answers positively a question raised by A. Kleinschmidt and D. Persson.

In the present paper it is proved that a variety of associative PI-superalgebras with graded involution finite basic rank over field characteristic zero minimal fixed *-graded exponent if, and only generated by subalgebra an upper block triangular matrix algebra equipped suitable elementary ?2-grading involution.

We study a family of symmetric functions $\hat F_z$ indexed by involutions $z$ in the affine group. These power series are analogues Lam's Stanley and generalizations involution introduced Hamaker, Pawlowski, first author. Our main result is to prove transition formula for which can be used define an analogue Lascoux-Sch\"utzenberger tree. proof this relies on Lam Shimozono's some new technical...

Let Λ be a ring endowed with an involution a 7→ ã. We say that two units a and b of Λ fixed under the involution are congruent if there exists an element u ∈ Λ× such that a = ubũ. We denote by H(Λ) the set of congruence classes. In this paper we consider the case where Λ is an order with involution in a semisimple algebraA over a local field and study the question whether the natural map H(Λ)→ ...