Shesh Raj Patel, Ajay Kumar Verma, Vijay Chandra Verma, Madhusudhana Reddy Janga and Gopal Nath* 1 Laboratory of Gastrointestinal Infections and Molecular Diagnosis, Department of Microbiology, Institute of Medical Sciences, Banaras Hindu University, Varanasi 221 005, UP India 2 Present address: AgriLife Research, Texas A& M University, College Station 77843, TX, USA 3 Institute for Plant Genom...

In this paper, we introduce baby Verma modules for symplectic reflection algebras of complex reflection groups at parameter t = 0 (the so–called rational Cherednik algebras at parameter t = 0) and present their most basic properties. As an example, we use baby Verma modules to answer several problems posed by Etingof and Ginzburg, [5], and give an elementary proof of a theorem of Finkelberg and...

The classical Rogers-Ramanujan identities have been interpreted by Lepowsky-Milne and the present authors in terms of the representation theory of the Euclidean Kac-Moody Lie algebra A(1) ((1)). Also, the present authors have introduced certain "vertex" differential operators providing a construction of A(1) ((1)) on its basic module, and Kac, Kazhdan, and we have generalized this construction ...

The branching problem for a couple of non-compatible Lie algebras and their parabolic subalgebras applied to generalized Verma modules was recently discussed in [15]. In the present article, we employ the recently developed F-method, [10], [11] to the couple of non-compatible Lie algebras Lie G2 i ↪→ so(7), and generalized conformal so(7)-Verma modules of scalar type. As a result, we classify t...

We show that the characters of all highest weight modules over an affine Lie algebra with the highest weight away from the critical hyperplane are meromorphic functions in the positive half of the Cartan subalgebra, their singularities being at most simple poles at zeros of real roots. We obtain some information about these singularities. 0. Introduction 0.0.1. Let g be a simple finite-dimensio...

R. Awasthi, A. Verma, V. K. Paliwal, S. K. Verma, K. N. Prasad, R. K. Rathore, and R. K. Gupta Department of Radiodiagnosis, Sanjay Gandhi Post Graduate Institute of Medical Sciences, Lucknow, Uttar Pradesh, India, Department of Microbiology, Sanjay Gandhi Post Graduate Institute of Medical Sciences, Lucknow, Uttar Pradesh, India, Department of Neurology, Sanjay Gandhi Post Graduate Institute o...

Chern-Schwartz-MacPherson (CSM) classes generalize to singular and/or noncompact varieties the classical total homology Chern class of the tangent bundle of a smooth compact complex manifold. The theory of CSM classes has been extended to the equivariant setting by Ohmoto. We prove that for an arbitrary complex algebraic manifold X, the homogenized, torus equivariant CSM class of a constructibl...