Related papers: A branching rule for partition complexes
Splint is a decomposition of root system into union of root systems. Splint of root system for simple Lie algebra appears naturally in studies of (regular) embeddings of reductive subalgebras. Splint can be used to construct branching…
A scheme to perform the Cartan decomposition for the Lie algebra su(N) of arbitrary finite dimensions is introduced. The schme is based on two algebraic structures, the conjugate partition and the quotient algebra, that are easily generated…
In this mostly expository article, we consider certain homological aspects of branching laws for representations of a group restricted to its subgroups in the context of $p$-adic groups. We follow our earlier paper, ICM 2018 proceedings,…
Using a calculus of variations approach, we determine the shape of a typical plane partition in a large box (i.e., a plane partition chosen at random according to the uniform distribution on all plane partitions whose solid Young diagrams…
By a result of Hemmer, every simple Specht module of a finite symmetric group over a field of odd characteristic is a signed Young module. While Specht modules are parametrized by partitions, indecomposable signed Young modules are…
This is a second paper in a series devoted to the minimal unitary representation of O(p,q). By explicit methods from conformal geometry of pseudo-Riemannian manifolds, we find the branching law corresponding to restricting the minimal…
To facilitate a simultaneous treatment of an arbitrary number of colors in representation theory-based descriptions of QCD color structure, we derive an $N$-independent reduction of SU($N$) tensor products. To this end, we label each…
We study the decomposition matrices for the unipotent $\ell$-blocks of finite special unitary groups SU$_n(q)$ for unitary primes $\ell$ larger than $n$. Up to very few unknown entries, we give a complete solution for $n=2,\ldots,10$. We…
The aim of this paper is to develop the combinatorics of constructions associated to what we call \emph{triangular partitions}. As introduced in arXiv:2102.07931, these are the partitions whose cells are those lying below the line joining…
We reconsider the relation of superconformal indices of superconformal field theories of class S with five-dimensional N=2 supersymmetric Yang-Mills theory compactified on the product space of a round three-sphere and a Riemann surface. We…
In this paper, we consider a subclass of quantum states in the multipartite system, namely, the supersymmetric states. We investigate the problem whether they admit the symmetrically separable decomposition, i.e., each term in this…
Kingman derived the Ewens sampling formula for random partitions from the genealogy model defined by a Poisson process of mutations along lines of descent governed by a simple coalescent process. M\"ohle described the recursion which…
We present an overview of results on branching laws for square integrable representations of a semisimple Lie group, restricted to a closed reductive subgroup. The overview is partial and it is based on joint work with Bent {\O}rsted and…
In this paper, we investigate $\pi(m,n)$, the number of partitions of the \emph{bipartite number} $(m,n)$ into \emph{steadily decreasing} parts, introduced by L.Carlitz ['A problem in partitions', Duke Math Journal 30 (1963), 203--213]. We…
The main purpose of this paper is to show that the mixed Hodge polynomial of the ``space of equations'' for smooth complete intersections of given multidegree in $\mathbb{C} P^n$ is divisible by the mixed Hodge polynomial of the group…
In this paper branching rules for the fundamental representations of the symplectic groups in positive characteristic are found. The submodule structure of the restrictions of the fundamental modules for the group $Sp_{2n}(K)$ to the…
For a partition {\lambda} and a prime p, we prove a necessary and sufficient condition for there exists a composition {\delta} such that {\delta} can be obtained from {\lambda} after rearrangement and all the partial sums of {\delta} are…
Our aim in this thesis is to use the language of deformation-quantization to understand certain quantized algebras by looking at properties of the corresponding commutative ones, and conversely to obtain results about the commutative…
In this paper, we obtain upper and lower bounds for the partition function $p(n)$ by using an elementary geometric inequality in Euclidean space, and we extend the method to generalizations of the partition function.
Splint of root system for simple Lie algebra appears naturally in studies of (regular) embeddings of reductive subalgebras. Splint can be used to construct branching rules. We demonstrate that splint properties implementation drastically…