相关论文: Supercharacter formulas for pattern groups
Let J be a finite-dimensional nilpotent algebra over a finite field F_q. We formulate a procedure for analysing characters of the group 1+J. In particular, we study characters of the group $U_n (q)$ of unipotent triangular $n\times n$…
It is proved the the restriction of any supercharacter of a finite group of triangular type on its subgroup is a sum of supercharacters with nonnegative integer coefficients. We define superinduction and prove the analog of the Frobenius…
We present an explicit formula for subregular characters (i.e, irreducible finite-dimensional complex characters of submaximal degree) of the unitriangular group over a finite field of sufficiently large characteristic.
We determine a supercharacter theory for the matrix Sylow $p$-subgroup ${^3}D_4^{syl}(q^3)$ of the Steinberg triality group ${^3}D_4(q^3)$, and establish the supercharacter table of ${^3}D_4^{syl}(q^3)$.
A general setting to study a certain type of formulas, expressing characters of the symmetric group $\mathfrak{S}_n$ explicitly in terms of descent sets of combinatorial objects, has been developed by two of the authors. This theory is…
The supercharacter theory of algebra groups gave us a representation theoretic realization of the Hopf algebra of symmetric functions in noncommuting variables. The underlying representation theoretic framework comes equipped with two…
The Jordan-H\"older Theorem is a general term given to a collection of theorems about maximal chains in suitably nice lattices. For example, the well-known Jordan-H\"older type theorem for chief series of finite groups has been rather…
The problem of computing the characters of the finite dimensional irreducible representations of the Lie superalgebra $\mathfrak q(n)$ over $\C$ was solved in 1996 by I. Penkov and V. Serganova. In this article, we give a different approach…
Let $N$ be a normal subgroup of a finite group $G$. From a result due to Brauer, it can be derived that the character table of $G$ contains square submatrices which are induced by the $G$-conjugacy classes of elements in $N$ and the…
We construct supercharacter theories for the finite groups constructed by parabolic constraction from simple groups of $A,B,C,D$ Lie types. In terms of rook placements in the root systems we classify supecharacters and superclasses.
We develop the theory of $q$-characters for quantum affine superalgebras of type $A$ in connection with deformed Cartan matrices. To achieve this, we establish a Khoroshkin-Tolstoy-type multiplicative formula of the universal $R$-matrix of…
In this paper, we study the vanishing-off subgroups of supercharacters, and use these to determine several new characterizations of supercharacter theory products. In particular, we give a character theoretic characterization that allows us…
In this paper we obtain the orthogonality relations for the supergroup U(m|n), which are remarkably different from the ones for the U(N) case. We extend our results for ordinary representations, obtained some time ago, to the case of…
The formulas for subregular characters of the unitriangular Lie group are obtained. The supports of regular and subregular characters are described in terms of the orbit method.
Words in some natural languages can have a composite structure. Elements of this structure include the root (that could also be composite), prefixes and suffixes with which various nuances and relations to other words can be expressed.…
We determine a supercharacter theory for Sylow $p$-subgroups ${^2{G}_2^{syl}(3^{2m+1})}$ of the Ree groups $^2{G}_2(3^{2m+1})$, calculate the conjugacy classes of ${^2{G}_2^{syl}(3^{2m+1})}$, and establish the character table of…
Isaacs has defined a character to be super monomial if every primitive character inducing it is linear. Isaacs has conjectured that if $G$ is an $M$-group with odd order, then every irreducible character is super monomial. We prove that the…
The classification of irreducible, spherical characters of the infinite-dimensional unitary/orthogonal/symplectic groups can be obtained by finding all possible limits of normalized, irreducible characters of the corresponding…
We provide a Hopf algebra structure on the space of superclass functions on the unipotent upper triangular group of type D over a finite field based on a supercharacter theory constructed by Andr\'e and Neto. Also, we make further comments…
We construct a family of orthogonal characters of an algebra group which decompose the supercharacters defined by Diaconis and Isaacs. Like supercharacters, these characters are given by nonnegative integer linear combinations of Kirillov…