Date & Time: Tuesday, July 22, 2008, 15:00-16:00.
Venue: Ramanujan Hall

Title: On the Redundancy of Higher Transvectants

Speaker: Jaydeep Chipalkatti, University of Manitoba

Abstract: Transvectants were introduced into algebra by the German school of invariant theorists in the nineteenth century. Given binary forms A and B of degrees m,n respectively,their rth transvectant Tr = (A,B)r is a new binary form of degree m+n-2r. In modern terminology, this construction encodes the multiplicative decomposition of representations for the algebraic group SL(2).

In this talk, I will explain the basic definitions and the role of transvectants in invariant theory. Our main theorem classifies all quadratic syzygies amongst the Tr. As a corollary, one can recover the higher transvectants T2 , T3 , ... etc from T0 and T1 alone. No substantial knowledge of algebraic geometry, or invariant theory will be presupposed.

All of this is joint work with Abdelmalek Abdesselam from the University of Virginia.