3.00 p.m.
PUBLIC VIVA-VOCE NOTIFICATION - Problems related to Invariant theory of Torus and finite groups
Santosha Kumar Pattanayak
Chennai Mathematical Institute.
24-06-11

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Abstract

The thesis studies two major problems in Invariant theory. One direction of our work takes is the study of projective normality of the polarized variety $(P(V)/G, \mathcal L)$, where $V$ is a finite dimensional representation of a finite group $G$ over a field $K$ and $\mathcal L$ is the descent of the line bundle $\mathcal O(1)^{\otimes |G|}$ ($\mathcal O(1)$ denotes the ample generator of the Picard group of $\mathbb P(V)$).

Another direction of our work is to study the semi-stable points for a maximal torus action on the homogeneous space $G/P$, where $G$ is semi-simple simply connected algebraic group and $P$ is a parabolic subgroup of $G$. Both studies arose out of an attempt to understand the quotient ${S_n}\backslash({T}\backslash \backslash G_{2,n})^{ss}$.