Algebra Seminar

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 r^th transvectant T_r = (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 T_r. 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.