Gladush∗, R.A. Konoplya Department ofPhysics,Dnepropetrovsk StateUniversity, per. 12 To what extent can one prescribe degrees of irreducible representations of a group? A good starting point for discussion the tensor product is the notion of direct sums. Which was interesting for me. We prove that the irreducible characters of the direct product … and tensor representations of groups V.D. We must add, the tensor product of two irreducible representations is not in general irreducible. Let G and H be groups that act compatibly on each other. Using the properties of the tensor product, it can be shown that these components satisfy the transformation law for a type (p, q) tensor. $\endgroup$ – … of Mathematics, University of Michigan, Ann Arbor MI 48109-1043. e-mail: … Introduction to the Tensor Product James C Hateley In mathematics, a tensor refers to objects that have multiple indices. We denote by η(G,H) a certain extension of the non-abelian tensor product G⊗H by G×H. Roughly speaking this can be thought of as a multidimensional array. Nauchny13,Dnepropetrovsk, 320625 Ukraine (April 16, 2018) Abstract There has been proposed a new method of the constructing of the basic functions for spaces of tensor representations of the Lie groups with the help Given two complex representations of two finite groups G_1 and G_2 on V_1 and V_2, we define their tensor product. Special Isogenies and Tensor Product Multiplicities Shrawan Kumar1 and John R. Stembridge2 1Department of Mathematics ,University of North Carolina Chapel Hill NC 27599-3250,and 2Department of Mathematics,University of Michigan,Ann Arbor MI 48109-1043 Correspondence to be sent to: John R. Stembridge, Dept. REMARK:The notation for each section carries on to the next. 1. History. Does the canonical basis of a tensor product of quantum group representations span the isotypic components of tilting modules? Suppose that G is residually finite and the subgroup [G,H]= g−1gh ∣g∈G,h∈H satisfies some non-trivial identity f≡ 1. ... Other classical groups have tensor representations, and so also tensors that are compatible with the group, but all non-compact classical groups have infinite-dimensional unitary representations as well. It decomposes into a direct sum of irreducible representations which can be determined by means of character theory, which we shall discuss in the next chapter. The tensor product of general groups really satisfies the universal property, due to the link in the answer of @3 1 3.