Related papers: Stabilized plethysms for the classical Lie groups

The decomposition of representations of compact classical Lie groups into representations of finite subgroups is discussed. A Mathematica package is presented that can be used to compute these branching rules using the Weyl character…

We consider the plethysm problem stated for representations of symmetric groups. In particular, we prove new relationships between composition multiplicities of twisted Foulkes modules. Expressed in terms of symmetric functions, our results…

Let $s_\nu \circ s_\mu$ denote the plethystic product of the Schur functions $s_\nu$ and $s_\mu$. In this article we define an explicit polynomial representation corresponding to $s_\nu \circ s_\mu$ with basis indexed by certain…

Kronecker coefficients encode the tensor products of complex irreducible representations of symmetric groups. Their stability properties have been considered recently by several authors (Vallejo, Pak and Panova, Stembridge). In previous…

We construct the polynomial induction functor, which is the right adjoint to the restriction functor from the category of polynomial representations of a general linear group to the category of representations of its Weyl group. This…

We use a plethystic formula of Littlewood to answer a question of Miller on embeddings of symmetric group characters. We also reprove a result of Miller on character congruences.

We introduce a basis of the symmetric functions that evaluates to the (irreducible) characters of the symmetric group, just as the Schur functions evaluate to the irreducible characters of $GL_n$ modules. Our main result gives three…

We show that continuous bounded group cohomology stabilizes along the sequences of real or complex symplectic Lie groups, and deduce that bounded group cohomology stabilizes along sequences of lattices in them, such as…

The Weyl modules in the sense of V.Chari and A.Pressley [CP] over the current Lie algebra on an affine variety are studied. We show that local Weyl modules are finite-dimensional and generalize the tensor product decomposition theorem from…

In 2015, the author proved combinatorially character formulas expressing sums of the (formal) dimensions of irreducible representations of symplectic groups, refining some works of Nekrasov and Okounkov, Han, King, and Westbury. In this…

We introduce a family of rings of symmetric functions depending on an infinite sequence of parameters. A distinguished basis of such a ring is comprised by analogues of the Schur functions. The corresponding structure coefficients are…

It is shown that a wide range of probabilities and limiting probabilities in finite classical groups have integral coefficients when expanded as a power series in 1/q. Moreover it is proved that the coefficients of the limiting…

In this paper, we prove several stability theorems for multiplicities of naturally defined representations of symmetric groups. The first such theorem states that if we consider the diagonal action of the symmetric group $S_{m+r}$ on $k$…

Following the general idea of Schur--Weyl scheme and using two suitable symmetric groups (instead of one), we try to make more explicit the classical problem of decomposing tensor representations of finite and infinite symmetric groups into…

Exploiting particular features of classical groups, simple constructions are given for the irreducible constituents of the tensor square of the adjoint modules and the leading terms in higher tensor powers. This provides an independent…

Gordon James proved that the socle of a Weyl module of a classical Schur algebra is a sum of simple modules labelled by $p$-restricted partitions. We prove an analogue of this result in the very general setting of "Schur pairs". As an…

Let B be a reductive Lie subalgebra of a semi-simple Lie algebra of the same rank both over the complex numbers. To each finite dimensional irreducible representation $V_\lambda$ of F we assign a multiplet of irreducible representations of…

One interesting combinatorial feature of classical determinantal varieties is that the character of their coordinate rings give a natural truncation of the Cauchy identity in the theory of symmetric functions. Natural generalizations of…

We determine the graded decompositions of fusion products of finite-dimensional irreducible representations for simple Lie algebras of rank two. Moreover, we give generators and relations for these representations and obtain as a…

The Newell-Littlewood numbers $N_{\mu,\nu,\lambda}$ are tensor product multiplicities of Weyl modules for classical Lie groups, in the stable limit. For which triples of partitions $(\mu,\nu,\lambda)$ does $N_{\mu,\nu,\lambda}>0$ hold? The…