Related papers: Andrews-Bressoud series and Wronskians
In type A, the q,t-Fuss-Catalan numbers can be defined as a bigraded Hilbert series of a module associated to the symmetric group. We generalize this construction to (finite) complex reflection groups and, based on computer experiments, we…
Using a specific form of the triple product identity, polygonal number identities are stated. Further number identities are examined that can be considered identities related to modular sets of numbers. The identities can be used to give…
Andrews and El Bachraoui recently studied integer partitions where the smallest part is repeated a specified number of times and any other parts are distinct. Their results included two ``surprising identities'' for which they requested…
Basic modules of McLain groups $M=M(\Lambda,\leq, R)$ are defined and investigated. These are (possibly infinite dimensional) analogues of Andr\'e's supercharacters of $U_n(q)$. The ring $R$ need not be finite or commutative and the field…
We prove a conjecture for the irreducibility of singular Gelfand-Tsetlin modules. We describe explicitly the irreducible subquotients of certain classes of singular Gelfand-Tsetlin modules.
We define a family of the braid group representations via the action of the $R$-matrix (of the quasitriangular extension) of the restricted quantum $\mathfrak{sl}(2)$ on a tensor power of a simple projective module. This family is an…
In his study of Nekrasov-Okounkov type formulas on "partition theoretic" expressions for families of infinite products, Han discovered seemingly unrelated $q$-series that are supported on precisely the same terms as these infinite products.…
Andrews and Merca introduced and proved a $q$-series expansion for the partial sums of the $q$-series in Euler's pentagonal number theorem. Kolitsch, in 2022, introduced a generalization of the Andrews-Merca identity via a finite sum…
Certain infinite families of operator identities related to powers of positive root generators of (super) Lie algebras of first-order differential operators and $q$-deformed algebras of first-order finite-difference operators are presented.
The affine vertex operator algebras for $\mathfrak{sl}_2$ and the Virasoro minimal models are related by Drinfeld-Sokolov reduction and by the Goddard-Kent-Olive coset construction. In this work, we propose another connection based on…
In 1984, Bressoud and Subbarao obtained an interesting weighted partition identity for a generalized divisor function, by means of combinatorial arguments. Recently, the last three named authors found an analytic proof of the aforementioned…
Many classical $q$-series identities, such as the Rogers--Ramanujan identities, yield combinatorial interpretations in terms of integer partitions. Here we consider algebraically manipulating some of the classical $q$-series to yield…
We study cylindric partitions with two-element profiles using MacMahon's partition analysis. We find explicit formulas for the generating functions of the number of cylindric partitions by first finding the recurrences using partition…
We study the unitarity and modularity of ribbon tensor categories derived from simple affine Lie algebras, via their associated quantum groups. Based on numerical calculations, and assuming two conjectures, we provide the complete picture…
We extend results of Andrews and Bressoud on the vanishing of coefficients in the series expansions of certain infinite products. These results have the form that if \begin{equation*} \frac{(q^{r-tk}, q^{mk-(r-tk)};…
We construct a new family of homomorphisms from Specht modules into Foulkes modules for the symmetric group. These homomorphisms are used to give a combinatorial description of the minimal partitions (in the dominance order) which label…
The main result describes the Brauer-Nesbitt reduction of unipotent representations of a finite group of Lie type, expressing it as an explicit linear combination of the restriction of Weyl modules from the algebraic group to the group of…
In previous work, the authors introduced the notion of Q-Koszul algebras, as a tool to "model" module categories for semisimple algebraic groups over fields of large characteristics. Here we suggest the model extends to small…
The purpose of this paper is to construct new families of irreducible Gelfand-Tsetlin modules for U_q(gl_n). These modules have arbitrary singularity and Gelfand-Tsetlin multiplicities bounded by 2. Most previously known irreducible modules…
In this article we aim to develop from first principles a theory of sum sets and partial sum sets, which are defined analogously to difference sets and partial difference sets. We obtain non-existence results and characterisations. In…