Related papers: On string functions and double-sum formulas
We discuss our conjecture for simply laced Lie algebras level two string functions of mark one fundamental weights and prove it for the $SO(2r)$ algebra. To prove our conjecture we introduce $q$-diagrams and examine the diagrammatic…
For a positive integer k and an arbitrary integer h, the Dedekind sum s(h,k) was first studied by Dedekind because of the prominent role it plays in the transformation theory of the Dedekind eta-function, which is a modular form of weight…
We study zeta functions enumerating finite-dimensional irreducible complex linear representations of compact p-adic analytic and of arithmetic groups. Using methods from p-adic integration, we show that the zeta functions associated to…
We calculate some infinite sums containing the digamma function in closed-form. These sums are related either to the incomplete beta function or to the Bessel functions. The calculations yield interesting new results as by-products, such as…
Smooth modules for affine Kac-Moody algebras have a prime importance for the quantum field theory as they correspond to the representations of the universal affine vertex algebras. But, very little is known about such modules beyond the…
We investigate spt-crank-type functions arising from Bailey pairs. We recall four spt-type functions corresponding to the Bailey pairs $A1$, $A3$, $A5$, and $A7$ of Slater and given four new spt-type functions corresponding to Bailey pairs…
We present completions of mock theta functions to harmonic weak Maass forms of weight $1/2$ and algebraic formulas for the coefficients of mock theta functions. We give several harmonic weak Maass forms of weight $1/2$ that have mock theta…
Two actions of the Hecke algebra of type A on the corresponding polynomial ring are studied. Both are deformations of the natural action of the symmetric group on polynomials, and keep symmetric functions invariant. We give an explicit…
This treatise investigates holomorphic functions defined on the space of bicomplex numbers introduced by Segre. The theory of these functions is associated with Fueter's theory of regular, quaternionic functions. The algebras of quaternions…
The direct sum of irreducible level one integrable representations of affine Kac-Moody Lie algebra of (affine) type $ADE$ carries a structure of $P/Q$-graded vertex operator algebra. There exists a filtration on this direct sum studied by…
We introduce a new generalisation of partitions, multi-grounded partitions, related to ground state paths indexed by dominant weights of Lie algebras. We use these to express characters of irreducible highest weight modules of Kac-Moody…
In this paper, we introduce formal sine functions whose coefficients are elements of a generalized harmonic algebra and investigate their properties corresponding to the classical addition formula and Pythagorean theorem. By taking their…
We construct indecomposable modules for the 0-Hecke algebra whose characteristics are the dual immaculate basis of the quasi-symmetric functions.
A procedure is described that makes use of the generating function of characters to obtain a new generating function $H$ giving the multiplicities of each weight in all the representations of a simple Lie algebra. The way to extract from…
We propose a conjecture refining the Stark conjecture St(K/k,S) (Tate's formulation) in the function field case. Of course St(K/k,S) in this case is a theorem due to Deligne and independently to Hayes. The novel feature of our conjecture is…
We introduce a new type of multiple zeta functions, which we call bilateral zeta functions, analogous to the Barnes zeta functions. The bilateral zeta function is a periodic function and shares certain basic properties of Barnes zeta…
This article introduces an algebra of functions in one variable $c$ defined by iterated integrals of two specific differential forms depending on $c$, where the product is the shuffle product. This algebra can be seen as a common…
We construct a family of exact functors from the BGG category of representations of the Lie algebra sl to the category of finite-dimensional representations of the degenerate (or graded) affine Hecke algebra H of GL. These functors…
We study a family of modules over Kac-Moody algebras realized in multi-valued functions on a flag manifold and find integral representations for intertwining operators acting on these modules. These intertwiners are related to some…
Mirror curves to toric Calabi-Yau threefolds can be quantized and lead to trace class operators on the real line. The eigenvalues of these operators are encoded in the BPS invariants of the underlying threefold, but much less is known about…