English Dictionary

symplectic group

noun

(linear algebra, group theory) For given field F and positive integer n, the group of 2n×2n symplectic matrices with elements in F.

The symplectic group is a fundamental concept in linear algebra.

意味（1）

(linear algebra, group theory) For given field F and positive integer n, the group of 2n×2n symplectic matrices with elements in F.

This representation ω arises by virtue of the existence of an action by automorphisms of the symplectic group on a certain two-step nilpotent group, commonly called the Heisenberg group.

This representation ω arises by virtue of the existence of an action by automorphisms of the symplectic group on a certain two-step nilpotent group, commonly called the Heisenberg group. Weil was of course working in the adelic formalism of modern number theory, so he considered symplectic groups and Heisenberg groups with coefficients in a general local field.