Related papers: The Bailey chain and mock theta functions
In this paper, we introduce $q$-analogues of the Barnes multiple zeta functions. We show that these functions can be extended meromorphically to the whole plane, and moreover, tend to the Barnes multiple zeta functions when $q\uparrow 1$…
It is known that characters of BPS representations of extended superconformal algebras do not have good modular properties due to extra singular vectors coming from the BPS condition. In order to improve their modular properties we apply…
In a previous paper we constructed $\textit{higher}$ theta series for unitary groups over function fields, and conjectured their modularity properties. Here we prove the generic modularity of the $\ell$-adic realization of higher theta…
Generalized trigonometric functions and generalized hyperbolic functions can be converted to each other by the duality formulas previously discovered by the authors. In this paper, we apply the duality formulas to prove dual pairs of…
We prove several infinite families of $q$-series identities for false theta functions and related series. These identities are motivated by considerations of characters of modules of vertex operator superalgebras and of quantum…
A family of tridiagonal pairs which appear in the context of quantum integrable systems is studied in details. The corresponding eigenvalue sequences, eigenspaces and the block tridiagonal structure of their matrix realizations with respect…
For the rational Baker-Akhiezer functions associated with special arrangements of hyperplanes with multiplicities we establish an integral identity, which may be viewed as a generalisation of the self-duality property of the usual Gaussian…
In a recent survey, Schmidt compiled equivalences between generalized bent functions, group invariant Butson Hadamard matrices, and abelian splitting relative difference sets. We establish a broader network of equivalences by considering…
We consider two important families of BC_n-symmetric polynomials, namely Okounkov's interpolation polynomials and Koornwinder's orthogonal polynomials. We give a family of difference equations satisfied by the former, as well as…
We analyze families of Markov chains that arise from decomposing tensor products of irreducible representations. This illuminates the Burnside-Brauer Theorem for building irreducible representations, the McKay Correspondence, and Pitman's…
A pair of sequences $(\alpha_{n}(a,k,q),\beta_{n}(a,k,q))$ such that $\alpha_0(a,k,q)=1$ and \[ \beta_{n}(a,k,q) = \sum_{j=0}^{n} \frac{(k/a; q)_{n-j}(k; q)_{n+j}}{(q;q)_{n-j}(aq;q)_{n+j}}\alpha_{j}(a,k,q) \] is termed a \emph{WP-Bailey…
We introduce generalized global Weyl modules and relate their graded characters to nonsymmetric Macdonald polynomials and nonsymmetric $q$-Whittaker functions. In particular, we show that the series part of the nonsymmetric $q$-Whittaker…
Asymptotic theory of tail index estimation has been studied extensively in the frequentist literature on extreme values, but rarely in the Bayesian context. We investigate whether popular Bayesian kernel mixture models are able to support…
Singular nonsymmetric Macdonald polynomials are constructed by use of the representation theory of the Hecke algebras of the symmetric groups. These polynomials are labeled by quasistaircase partitions and are associated to special…
Bayesian statistical models allow us to formalise our knowledge about the world and reason about our uncertainty, but there is a need for better procedures to accurately encode its complexity. One way to do so is through compositional…
Two approaches to studying the correlation functions of the binary Markov sequences are considered. The first of them is based on the study of probability of occurring different ''words'' in the sequence. The other one uses recurrence…
We characterize the theta functions for vectors in the imaginary wall in a cluster algebra of acyclic affine type and compute some of their structure constants. One of the structure constant computations can be interpreted as new…
The Mackey-type identity mentioned in the title relates the operations of parabolic induction and restriction for invariant functions on the Lie algebras of the finite unitary groups $U(N, q^2)$. This result is applied to constructing…
We provide a framework for relating certain q-series defined by sums over partitions to multiple zeta values. In particular, we introduce a space of polynomial functions on partitions for which the associated q-series are q-analogues of…
A unified algebraic interpretation of both finite families of orthogonal polynomials and biorthogonal rational functions of $q$-Hahn type is provided. The approach relies on the meta $q$-Hahn algebra and its finite-dimensional bidiagonal…