相关论文: Tensor powers of representations of (diagram) mono…
We introduce and study several affine (=annular in this paper) versions of the classical diagram algebras such as Temperley-Lieb, partition, Brauer, Motzkin, rook Brauer, rook, planar partition, and planar rook algebras. We give generators…
In this paper we study the asymptotic behavior of the number of summands in tensor products of finite dimensional representations of affine (semi)group (super)schemes and related objects.
Tensor products of quiver representations have been extensively studied; typical examples include the pointwise tensor product and the tensor product induced by the coalgebra structure of path algebras. In this paper, we investigate the…
We classify and enumerate the idempotents in several planar diagram monoids: namely, the Motzkin, Jones (a.k.a. Temperley-Lieb) and Kauffman monoids. The classification is in terms of certain vertex- and edge-coloured graphs associated to…
The non-empty finite subsets of a multiplicatively written monoid form a monoid under setwise multiplication. The same holds for finite subsets containing the identity element. Partly due to their unusual arithmetic properties, these…
We give explicit formulas for the asymptotic growth rate of the number of summands in tensor powers in certain monoidal categories with finitely many indecomposable objects, and related structures.
We consider the problem of determining the relationship between two representations knowing that some tensor or symmetric power of the original represetations coincide. Combined with refinements of strong multiplicity one, we show that if…
We give a complete description of the congruence lattices of the following finite diagram monoids: the partition monoid, the planar partition monoid, the Brauer monoid, the Jones monoid (also known as the Temperley-Lieb monoid), the Motzkin…
We give a general asymptotic formula for the growth rate of the number of indecomposable summands in the tensor powers of representations of finite groups, over a field of arbitrary characteristic. In characteristic zero we obtain…
We study the number of indecomposable summands in tensor powers of the vector representation of SL2. Our main focus is on positive characteristic where this sequence of numbers and its generating function show fractal behavior akin to…
We give a decomposition formula for tensor powers of the defining representation of $S_n$ and apply it to bound the mixing time of a Markov chain on $S_n$.
We discuss formulas for the asymptotic growth rate of the number of summands in tensor powers in certain (finite or infinite) monoidal categories. Our focus is on monoidal categories with infinitely many indecomposable objects, with our…
We study representations of diagram categories by binary relations and matrices over rings and semirings. Our main result is a faithful involutive tensor representation of the partition category $P$ (and consequently of each partition…
We obtain formulae for the minimum transformation degrees of the most well-studied families of finite diagram monoids, including the partition, Brauer, Temperley--Lieb and Motzkin monoids. For example, the partition monoid $P_n$ has degree…
We study monoids generated by various combinations of idempotents and one- or two-sided units of an infinite partial Brauer monoid. This yields a total of eight such monoids, each with a natural characterisation in terms of relationships…
We construct a faithful categorical representation of an infinite Temperley-Lieb algebra on the periplectic analogue of Deligne's category. We use the corresponding combinatorics to classify thick tensor ideals in this periplectic Deligne…
We give a characterisation of the idempotents of the partition monoid, and use this to enumerate the idempotents in the finite partition, Brauer and partial Brauer monoids, giving several formulae and recursions for the number of…
We study a composition operation on monads, equivalently presented as large equational theories. Specifically, we discuss the existence of tensors, which are combinations of theories that impose mutual commutation of the operations from the…
This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models---including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation---which…
We define new norms for symmetric tensors over ordered normed spaces; these norms are defined by considering linear combinations of tensor products or powers of positive elements only. Relations between the different norms are studied. The…