2 citations · 8 across the 9 of their papers we have counts for
11 papers
Characteristic polynomials and finitely dimensional representations of simple Lie Algebras
Amin Geng, Shoumin Liu, Xumin Wang
In this paper, the correspondence between the finite dimensional representations of a simple Lie algebra and their characteristic polynomials is established, and a monoid structure…
Characteristic polynomials and finitely dimensional representations of
Tianyi Jiang, Shoumin Liu
In this paper, we obtain a general formula for the characteristic polynomial of a finitely dimensional representation of Lie algebra $\mathfrak{sl}(2, \C )$ and the form for these…
Morita equivalences on Brauer algebras and BMW algebras of simply-laced types
Shoumin Liu
The Morita equivalences of classical Brauer algebras and classical Birman-Murakami-Wenzl algebras have been well studied. Here we study the Morita equivalence problems on these two…
The Dieck-Temperley-Lieb algebras in Brauer algebras
Shoumin Liu
In this paper, we will study the Dieck-Temlerley-Lieb algebras of type Bn and Cn. We compute their ranks and describe a basis for them by using some results from corresponding Brau…
Clifford theory on rational Cherednik algebras of imprimitive groups
Shoumin Liu
Ram and Rammage have introduced an automorphism and Clifford theory on affine Hecke algebras. Here we will extend them to cyclotomic Hecke algebras and rational Cherednik algebras.
Brauer Algebras of multiply laced Weyl type
Shoumin Liu
In this paper, we will define the Brauer algebras of Weyl types, and describe some propositions of these algebras. Especially, we prove the result of type to accomplish our p…
Brauer algebras of type H3 and H4
Shoumin Liu
In this paper, we will present Brauer algebras associated to spherical Coxeter groups of type H3 and H4, which are also can be regarded as subalgebras of Brauer algebras D6 and E8…
Brauer algebra of type I2n
Shoumin Liu
We will present an algebra related to the Coxeter group of type I2n which can be taken as a twisted subalgebra in Brauer algebra of type A_{n-1}. Also we will describe some propert…
Brauer algebra of type F4
Shoumin Liu
We present an algebra related to the Coxeter group of type F4 which can be viewed as the Brauer algebra of type F4 and is obtained as a subalgebra of the Brauer algebra of type E6.…
Brauer algebras of type B
Arjeh M. Cohen, Shoumin Liu
For each n>0, we define an algebra having many properties that one might expect to hold for a Brauer algebra of type Bn. It is defined by means of a presentation by generators and…
Brauer algebras of type C
Arjeh M. Cohen, Shoumin Liu, Shona Yu
For each natural number n greater than 1, we define an algebra satisfying many properties that one might expect to hold for a Brauer algebra of type Cn. The monomials of this algeb…