Related papers: Multiplicity, Invariants and Tensor Product Decomp…

In this paper, we introduce a study of prolongations of representations of Lie groups. We obtain a faithful (one-to-one) representation of TG where G is a finite-dimensional Lie group and TG is the tangent bundle of G, by using (not…

In this paper we study irreducible tensor products of representations of alternating groups and classify such products in characteristic 5.

Real or complex tensor model observables, the backbone of the tensor theory space, are classical (unitary, orthogonal, symplectic) Lie group invariants. These observables represent as colored graphs, and that representation gives an handle…

We introduce a nonsymmetric, associative tensor product among representations of Cuntz algebras by using embeddings. We show the decomposition formulae of tensor products for permutative representations explicitly We apply decomposition…

Tensor products of irreducible representations of the Jordanian quantum algebras U_h(sl(2)) and U_h(su(1,1)) are considered. For both the highest weight finite dimensional representations of U_h(sl(2)) and lowest weight infinite dimensional…

Tensor products of ultrafilters have special combinatorial features closely related to Ramsey's Theorem, making them useful tools in applications. Here we first review their fundamental properties and isolate some new ones, including a…

In this paper we study modular tensor categories (braided rigid balanced tensor categories with additional finiteness and non-degeneracy conditions), in particular, representations of quantum groups at roots of unity. We show that the…

We study irreducible unitary \reps of $U_q(SO(2,1))$ and $U_q(SO(2,3))$ for $q$ a root of unity, which are finite dimensional. Among others, unitary \reps corresponding to all classical one-particle representations with integral weights are…

Let K be the product O(n_1) x O(n_2) x ... x O(n_r) of orthogonal groups. Let V the r-fold tensor product of defining representations of each orthogonal factor. We compute a stable formula for the dimension of the K-invariant algebra of…

In this paper we consider the problem of decomposing tensor products of certain singular unitary representations of a semisimple Lie group G. Using explicit models for these representations (constructed earlier by one of us) we show that…

We construct a class of negative spin irreducible representations of the su(2) Lie algebra. These representations are infinite-dimensional and have an indefinite inner product. We analyze the decomposition of arbitrary products of positive…

We show that a tensor product of irreducible, finite dimensional representations of a simple Lie algebra over a field of characteristic zero, determines the individual constituents uniquely. This is analogous to the uniqueness of prime…

We prove that for a suitable class of representations of free group tensor products are generically irreducible. In particular we prove that there exist irreducible boundary realizations with infinite dimensional fiber.

We present a conjecture on the irreducibility of the tensor products of fundamental representations of quantized affine algebras. This conjecture implies in particular that the irreducibility of the tensor products of fundamental…

In this paper, we consider the necessary and sufficient conditions for the tensor product of the fundamental representations for the restricted quantum loop algebras of type A at roots of unity to be irreducible.

We define and study a certain relative tensor product of subfactors over a modular tensor category. This gives a relative tensor product of two completely rational heterotic full local conformal nets with trivial superselection structures…

We give a description of the image of tensor products of tautological bundles on Hilbert schemes of points on surfaces under the Bridgeland-King-Reid-Haiman equivalence. Using this, some new formulas for cohomological invariants of these…

We initiate a study of infinite tensor products of projective unitary representations of a discrete group G. Special attention is given to regular representations twisted by 2-cocycles and to projective representations associated with…

$U(N)^{\otimes r} \otimes O(N)^{\otimes q}$ invariants are constructed by contractions of complex tensors of order $r+q$, also denoted $(r,q)$. These tensors transform under $r$ fundamental representations of the unitary group $U(N)$ and…

We show that every admissible irreducible representation of a product of two locally compact groups is a tensor product of admissible irreducible representations of the factors.