We prove a Schur-Weyl duality between the quantum enveloping algebra of $\mathfrak{gl}_m$ and certain quotient algebras Ariki-Koike algebras, which we give explicitly. The involves several algebraically independent parameters is realized through tensor product parabolic universal Verma module power natural representation $\mathfrak{gl}_m$. also new presentation by generators relations generaliz...

In 1939 Rademacher demonstrated how to express Klein’s modular invariant as a sum over elements of the modular group. In this article we generalize Rademacher’s approach so as to construct bases for the spaces of automorphic integrals of arbitrary even integer weight, for an arbitrary group commensurable with the modular group. Our methods provide explicit expressions for the Fourier expansions...

Affine Lie algebras admit non-classical highest-weight theories through alternative partitions of the root system. Although significant inroads have been made, much of the classical machinery is inapplicable in this broader context, and some fundamental questions remain unanswered. In particular, the structure of the reducible objects in non-classical theories has not yet been fully understood....

We construct a family of exact functors from the BernsteinGelfand-Gelfand category O of sln-modules to the category of finite-dimensional representations of the degenerate affine Hecke algebra Hl of GLl. These functors transform Verma modules to standard modules or zero, and simple modules to simple modules or zero. Any simple Hl-module can be thus obtained. Introduction The classical Frobenius...

In [Zh], R. B. Zhang found a way to link certain formal deformations of the Lie algebra o(2l + 1) and the Lie superalgebra osp(1, 2l). The aim of this article is to reformulate the Zhang transformation in the context of the quantum enveloping algebrasà la Drinfeld-Jimbo and to show how this construction can explain the main theorem of [GL2]: the annihilator of a Verma module over the Lie supera...

Biofertilizers are living microorganisms; they themselves are not source of nutrients but can help the plant in accessing the nutrient available in its surrounding environments (Suman et al., 2015). In general, commonly microbes used as biofertilizers may be Azotobacter, Azospirillum, Rhizobium as nitrogen fixing soil bacteria (Verma et al., 2013, 2014; Verma et al., 2015; Verma et al., 2016a);...

We introduce a suitable adapted ordering for the twisted N = 2 superconformal algebra (i.e. with mixed boundary conditions for the fermionic fields). We show that the ordering kernels for complete Verma modules have two elements and the ordering kernels for G-closed Verma modules just one. Therefore, spaces of singular vectors may be two-dimensional for complete Verma modules whilst for G-close...