UNC Algebraic Geometry Talk
Friday, October 15, 1999, 3:00pm, Phillips Hall, UNC
(at UNC) A.J. Parameswaran (T.I.F.R.--Bombay)
Semistability of Induced Bundles Under a Low Height Representation

Abstract:

For a connected reductive algebraic group $G$, over an algebraically closed field $k$ of charecteristic $p>0$, the semisimplicity and the semistability of induced budlles are closely related with the heights of dominant integral weights occuring there. The height of a weight $ht(\lambda)$ is the sum of the coefficients of an expression as sum simple roots. A representation is low height if every weight $\lambda$ occuring in $V$ satisfies $2ht(\lambda)\gamma(G)$ and $V$ a representation not of low height. Then there exists a curve $X$ and a semistable $G$-bundle on $X$ such that the induced principal bundle $E(SL(V))$ is not semistable. Moreover we also a complete reducibility result for non-reduecd groups which occur as stabilizers of vectors under low height representations. This results imply that we can have also a polystability (i.e., stable bundles inducing direct sum of stable bundles) result. As another application is to get Luna's etal slice theorem in positive charecteristic for low height representations.

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