Equality of Linear and Symplectic Orbits

Pratyusha Chattopadhyay; Ravi A. Rao

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arXiv · 1108.1288

Equality of Linear and Symplectic Orbits

Pratyusha Chattopadhyay·Ravi A. Rao

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Abstract

It is shown that the set of orbits of the action of the elementary symplectic transvection group on all unimodular elements of a symplectic module over a commutative ring of characteristic not 2 is identical with the set of orbits of the action of the corresponding elementary transvection group. This result is used to get improved injective stability estimates for $K_1$ of the symplectic transvection group over a non-singular affine algebras.

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Pratyusha Chattopadhyay, Ravi A. Rao. 2015-03-25. Equality of Linear and Symplectic Orbits. https://arxiv.org/abs/1108.1288

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