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We prove a theorem about the derivation algebra of the tensor product of two algebras. As an application, we determine the derivation algebra of the fixed point algebra of the tensor product of two algebras, with respect to the tensor…
We study irreducible restrictions from modules over alternating groups to subgroups. We get reduction results which substantially restrict the classes of subgroups and modules for which this is possible. This is known when the…
In this paper we study obstructions to presentability by products for finitely generated groups. Along the way we develop both the concept of acentral subgroups, and the relations between presentability by products on the one hand, and…
We propose a set of 4 recurrence relations whose linear combination gives the number of group invariants, equivalently the dimension of the invariant subspace, in the tensor product of an arbitrary number of adjoint representations of the…
The transformation properties of irreducible tensor operators and the applicability of the Wigner-Eckart theorem to finite magnetic groups have been studied.
We classify the irreducible finite-dimensional representations of the twisted quantum affine algebras.
We determine precisely the number of irreducible summands of an irreducible cross characteristic representation of $GL_{n}(q)$ on restriction to $SL_{n}(q)$. Combined with a recent result of C. Bonnafe, this yields a canonical labeling for…
We survey tensor products of lattices with zero and related constructions focused on two topics: amenable lattices and box products.
In this paper the author finds explicitly all finite-dimensional irreducible representations of a series of finite permutation groups that are homomorphic images of Artin braid group.
A complex irreducible character of a finite group G is said to be p-constant, for some prime p dividing the order of G, if it takes constant value at the set of p-singular elements of G. In this paper we classify irreducible p-constant…
In this paper, we consider the construction of irreducible representations of finite pattern groups in terms of Panov's associative polarization, which is a finite-field analogue of Kirillov's orbital method. Using this construction, first,…
A novel combinatorial formula is developed for for tensor product multiplicities in representation theory. We introduce a difference formula linking these multiplicities to restricted occupancy coefficients via a shifted operator. This…
We prove a super-rigidity result for algebraic representations over complete fields of irreducible lattices in product of groups and lattices with dense commensurator groups. We derive some criteria for non-linearity of such groups.
We prove for residually finite groups the following long standing conjecture: the number of twisted conjugacy classes of an automorphism of a finitely generated group is equal (if it is finite) to the number of finite dimensional…
The irreducible representations of the group C4(direct product)V can be used to distinguish polarization eigenmodes, to account for their degeneracies and to associate them with particular magnetic crystal classes. The occurrence of this…
We classify irreducible representations of connected compact Lie groups whose orbit space is isometric to the orbit space of a representation of a finite extension of (positive dimensional) toric group. They turn out to be exactly the…
In this paper, we study the tensor structure of category of finite dimensional representations of Drinfeld quantum doubles $D(H_n(q))$ of Taft Hopf algebras $H_n(q)$. Tensor product decomposition rules for all finite dimensional…
In this article, we study the Schur mutiplier of the discrete as well as the finite Heisenberg groups and their t-variants. We describe the representation groups of these Heisenberg groups and through these give a construction of their…
We study a vertex operator algebra containing a tensor product of Ising models. It is a direct sum of code vertex operator algebra and its irreducible modules. Therefore, we classify all irreducible modules of code vertex operator algebras…
An analogue of Burnside's Lemma for 2-transitive groups is shown to hold for a class of topological groups. If the group is compact the representation is finite and splits into an irreducible and the constant functions. If both the group…