Related papers: A classical $q$-hypergeometric approach to the sta…

We give an a priori proof of the known presentations of (that is, completeness of families of relations for) the principal subspaces of all the standard A_1^(1)-modules. These presentations had been used by Capparelli, Lepowsky and Milas…

We show connection formulae of local solutions of the Ramanujan equation between the origin and the infinity. These solutions are given by the Ramanujan function, the $q$-Airy function and the divergent basic hypergeometric series…

In this paper, we will introduce the concept of classical (resp. strongly classical) 2-absorbing second submodules of modules over a commutative ring as a generalization of 2-absorbing (resp. strongly 2-absorbing) second submodules and…

The dominant dimension of algebras in the class A of 1-quasi-hereditary algebras is at least two. By the Morita-Tachikawa Theorem this implies that A is related to a certain class B of algebras via bimodules satisfying the double…

Presented are polynomial identities which imply generalizations of Euler and Rogers--Ramanujan identities. Both sides of the identities can be interpreted as generating functions of certain restricted partitions. We prove the identities by…

Feigin-Stoyanovsky's type subspaces for affine Lie algebras of type $C_\ell^{(1)}$ have monomial bases with a nice combinatorial description. We describe bases of whole standard modules in terms of semi-infinite monomials obtained as "a…

Using completions of certain universal enveloping algebras, we provide a natural setting for families of defining relations for the principal subspaces of standard modules for untwisted affine Lie algebras. We also use the theory of vertex…

In this paper, we introduce the notion of standard homogeneous $(\alpha_1,\alpha_2)$-metrics, as a natural non-Riemannian deformation for the normal homogeneous Riemannian metrics. We prove that with respect to the given bi-invariant inner…

Khovanov-Lauda-Rouquier algebras $R_\theta$ of finite Lie type are affine quasihereditary with standard modules $\Delta(\pi)$ labeled by Kostant partitions of $\theta$. Let $\Delta$ be the direct sum of all standard modules. It is known…

This is a companion article to my papers on Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebras gl(m|n) (much revised!) and q(n). The goal is to develop the general theory of tilting modules for Lie superalgebras,…

The paper contains a survey of the results obtained by the author in recent years. These results concern the application in multivariate polynomial interpolation of some geometric constructions and methods. In particular, we give estimates…

Slater's list of Rogers-Ramanujan type identities consists of 130 series-product identities whose analytic proofs rely primarily on Bailey pair techniques. Although these identities play an important role in the theory of $q$-series and…

This paper is concerned with a class of partition functions $a(n)$ introduced by Radu and defined in terms of eta-quotients. By utilizing the transformation laws of Newman, Schoeneberg and Robins, and Radu's algorithms, we present an…

We study graded rings of meromorphic Hermitian modular forms of degree two whose poles are supported on an arrangement of Heegner divisors. For the group $\mathrm{SU}_{2,2}(\mathcal{O}_K)$ where $K$ is the imaginary-quadratic number field…

Using a pair of two variable series-product identities recorded by Ramanujan in the lost notebook as inspiration, we find some new identities of similar type. Each identity immediately implies an infinite family of Rogers-Ramanujan type…

Feigin-Stoyanovsky's type subspace $W(\Lambda)$ of a standard $\tilde{{\mathfrak g}}$-module $L(\Lambda)$ is a $\tilde{{\mathfrak g}}_1$-submodule of $L(\Lambda)$ generated by the highest-weight vector $v_\Lambda$, where $\tilde{{\mathfrak…

We prove a q-series identity that generalises Macdonald's A_{2n}^{(2)} eta-function identity and the Rogers-Ramanujan identities. We conjecture our result to generalise even further to also include the Andrews-Gordon identities.

We provide a classification of generalized tilting modules and full exceptional sequences for the dual extension algebra of the path algebra of a uniformly oriented linear quiver modulo the ideal generated by paths of length two with its…

We systematically extend the elementary differential and Riemannian geometry of classical $\mathrm{U}(1)$-gauge theory to the noncommutative setting by combining recent advances in noncommutative Riemannian geometry with the theory of…

A distinctive problem of harmonic analysis on $\R$ with respect to a Borel probability measure $\mu$ is identifying all $t\in\R$ such that both \[\left\{e^{-2\pi i\lambda x}: \lambda\in\Lambda\right\}\quad\text{and}\quad \left\{e^{-2\pi…