In this thesis, we have tried to understand the geometry of normed spaces in the light of Birkhoff-James orthogonality. Using the first two chapters to give introductory notes and to establish relevant notations and ...

In this thesis, we study some important classification problems related to affine Kac--Moody Lie algebras. First, we address the combinatorial problem of classifying symmetric real-closed subsets of affine root systems ...

This thesis focuses on the study of specialized characters of irreducible polynomial representations of the complex classical Lie groups of types A, B, C and D. We study various specializations where the characters are ...

This thesis concerns the construction of harmonic maps from certain non-compact surfaces into hyperbolic 3-space H3 with prescribed asymptotic behavior and has two parts. The focus of the first part is when the domain ...

Let $\Omega \subseteq \mathbb C^m$ be a bounded connected open set and $\mathcal H \subseteq \mathcal O(\Omega)$ be an analytic Hilbert module, i.e., the Hilbert space $\mathcal H$ possesses a reproducing kernel $K$, the ...