Related papers: On character table of Clifford groups
Supergroups are defined in the framework of $\dZ_2$-graded Clifford algebras over the fields of real and complex numbers, respectively. It is shown that cyclic structures of complex and real supergroups are defined by Brauer-Wall groups…
We continue the study of glider representations of finite groups $G$ with given structure chain of subgroups $e \subset G_1 \subset \ldots \subset G_d = G$. We give a characterization of irreducible gliders of essential length $e \leq d$…
Clifford algebras are naturally associated with quadratic forms. These algebras are Z_2-graded by construction. However, only a Z_n-gradation induced by a choice of a basis, or even better, by a Chevalley vector space isomorphism Cl(V) <->…
In groups with involution a nonassociative product of elements is defined, which leads to the definition of a certain type of quasigroups. These quasigroups are represented by square tables of complex numbers, with inverses, which differ…
Quaternionic representations of Coxeter (reflection) groups of ranks 3 and 4, as well as those of E_8, have been used extensively in the literature. The present paper analyses such Coxeter groups in the Clifford Geometric Algebra framework,…
For any Kahler surface which admits no nonzero holomorphic vectorfields, we consider the group of holomorphic automorphisms which induce identity on the second rational cohomology. Assuming the canonical linear system is without base points…
The representation theory of the Clifford group is playing an increasingly prominent role in quantum information theory, including in such diverse use cases as the construction of protocols for quantum system certification, quantum…
The method of little groups describes the irreducible characters of semidirect products with abelian normal subgroups in terms of the irreducible characters of the factor groups. We modify this method to construct supercharacter theories of…
One particular approach to quantum groups (matrix pseudo groups) provides the Manin quantum plane. Assuming an appropriate set of non-commuting variables spanning linearly a representation space one is able to show that the endomorphisms on…
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…
A real representation theory of real Clifford algebra has been studied in further detail, especially in connection with Fierz identities. As its application, we have constructed real octonion algebras as well as related octonionic triple…
Let $\chi$ be a complex irreducible character of a finite group $G$. The conductor of $\chi$, denoted $c(\chi)$, is the smallest positive integer $n$ such that $\chi(x)\in \mathbb{Q}(\exp({2\pi i/n}))$ for all $x\in G$. We show that for…
We show how for $n=2,3 (\mod 4)$ continuous Clifford (geometric) algebra (GA) $Cl_n$-valued admissible wavelets can be constructed using the similitude group $SIM(n)$. We strictly aim for real geometric interpretation, and replace the…
We study asymptotics of an irreducible representation of the symmetric group S_n corresponding to a balanced Young diagram \lambda (a Young diagram with at most C\sqrt{n} rows and columns for some fixed constant C) in the limit as n tends…
Let $M^n$ be a compact hypersurface with constant mean curvature $H$ in $\mathbb{S}^{n+1}$. Denote by $S$ the squared norm of the second fundamental form of $M$. We prove that there exists a positive constant $\gamma(n)$ depending only on…
A complete classification is given of all inner actions on the Clifford algebra C(1,3) defined by representations of the quantum group GL_q(2,C), q^m\neq 1, which are not reduced to representations of two commuting "q-spinors". As a…
Let C_n denote the representation category of a finite supergroup generated by purely odd n-dimensional vector space. We compute the Brauer-Picard group BrPic(C_n) of C_n. This is done by identifying BrPic(C_n) with the group of braided…
Let G be a semisimple almost simple algebraic group defined and split over a nonarchimedean local field K and let S be the Steinberg representation of G(K). Let t be be a very regular semisimple element of G(K). In this paper we give a…
Composing with the inclusion $\mathsf{Set}\to\mathsf{Cat} $, a graph $G$ internal to $\mathsf{Set} $ becomes a graph of discrete categories, the coinserter of which is the category freely generated by $G$. Introducing a suitable definition…
In this paper we prove isomorphisms between 5 Lie groups (of arbitrary dimension and fixed signatures) in Clifford algebra and classical matrix Lie groups - symplectic, orthogonal and linear groups. Also we obtain isomorphisms of…