相关论文: Fusion procedure for Yokonuma-Hecke algebras
A complete system of primitive pairwise orthogonal idempotents for cyclotomic Hecke algebras is constructed by consecutive evaluations of a rational function in several variables on quantum contents of multi-tableaux. This function is a…
Inspired by the work [IMOg2], in this note, we prove that the pairwise orthogonal primitive idempotents of generic cyclotomic Birman-Murakami-Wenzl algebras can be constructed by consecutive evaluations of a certain rational function. In…
We establish two versions of the fusion procedure for the walled Brauer algebras. In each of them, a complete system of primitive pairwise orthogonal idempotents for the walled Hecke algebra is constructed by consecutive evaluations of a…
A complete system of pairwise orthogonal minimal idempotents for Birman-Murakami-Wenzl algebras is obtained by a consecutive evaluation of a rational function in several variables on sequences of quantum contents of up-down tableaux. A…
In this note, we first prove that the degenerate cyclotomic Yokonuma-Hecke algebra $Y_{r,n}^{d}$ is cellular by constructing an explicit cellular basis. We then develop the fusion procedure for $Y_{r,n}^{d}$, that is, a complete set of…
The primitive idempotents of the generic degenerate cycloctomic Hecke algebras are derived by consecutive evaluations of a certain rational function. This rational function depends only on the Specht modules and the normalization factors…
We give a new construction of primitive idempotents of the Hecke algebras associated with the symmetric groups. The idempotents are found as evaluated products of certain rational functions thus providing a new version of the fusion…
A complete system of primitive pairwise orthogonal idempotents for the Coxeter groups of type $B$ and, more generally, for the complex reflection groups $G(m,1,n)$ is constructed by a sequence of evaluations of a rational function in…
We show that all primitive idempotents for the Brauer algebra B_n(w) can be found by evaluating a rational function in several variables which has the form of a product of R-matrix type factors. This provides an analogue of the fusion…
We give a new fusion procedure for the Brauer algebra by showing that all primitive idempotents can be found by evaluating a rational function in several variables which has the form of a product of R-matrix type factors. In particular,…
Let G be a finite group. A complete system of pairwise orthogonal idempotents is constructed for the wreath product of G by the symmetric group by means of a fusion procedure, that is by consecutive evaluations of a rational function with…
We provide an explicit construction for a complete set of orthogonal primitive idempotents of finite group algebras over nilpotent groups. Furthermore, we give a complete set of matrix units in each simple epimorphic image of a finite group…
We construct a recursive formula for a complete system of primitive orthogonal idempotents for any $R$-trivial monoid. This uses the newly proved equivalence between the notions of $R$-trivial monoid and weakly ordered monoid.
Any multiplicity-free family of finite dimensional algebras has a canonical complete set of of pairwise orthogonal primitive idempotents in each level. We give various methods to compute these idempotents. In the case of symmetric group…
A complete set of primitive orthogonal idempotents plays an important role in the representation theory of an associative algebra. In this paper, we construct a complete set of primitive orthogonal idempotents for any finite Brandt…
We consider the algorithmic problem of computing a primitive idempotent of a central simple algebra over the field of rational functions over a finite field. The algebra is given by a set of structure constants. The problem is reduced to…
Building on the work of P.N. Norton, we give combinatorial formulae for two maximal decompositions of the identity into orthogonal idempotents in the $0$-Hecke algebra of the symmetric group, $\mathbb{C}H_0(S_N)$. This construction is…
In this paper, we explore the use of path idempotents for the Hecke algebra of type $A$ at roots of unity. For $q$ a primitive $\ell$-th root of unity we obain a non-unital imbedding of (a quotient of) the group algebra of $S_m$ into (a…
For a field $F$ and an integer $d\geq 1$, we consider the universal associative $F$-algebra $A$ generated by two sets of $d+1$ mutually orthogonal idempotents. We display four bases for the $F$-vector space $A$ that we find attractive. We…
We present a method to explicitly compute a complete set of orthogonal primitive idempotents in a simple component with Schur index 1 of a rational group algebra $\mathbb{Q}G$ for $G$ a finite generalized strongly monomial group. For the…