We prove uniqueness of Fourier Jacobi models for general linear groups, unitary groups, symplectic groups and metaplectic groups, over an Archimedean local field.
Since in a group every element has to be invertible, the most general matrix groups are the groups of all invertible matrices of a given size, called the general linear groups.
(PGL_n q)) denotes the projective general linear group of degree n over the field of order q.
It is well known that any vector pair spanned a plane section in (S TM)) are related by a general linear group (operatorname{GL}(2,mathbb{R})).
Let G1 be the subgroup of the general linear group GL ( g ) Open image in new window consisting of the elements which leaves I e invariant.
(S_n) means a symmetric group of degree n. (A_n) denotes the alternating group of degree n. (GL_n q)) denotes the general linear group of degree n over the field of order q.
The set of nonsingular square matrices forms a Lie group where the group product is modeled by matrix multiplication, usually denoted by for the general linear group of the order.
Let GL n Open image in new window be the general linear group of order n over Open image in new window, where n can be finite or infinite.
Let M be a connected manifold and G be a closed Lie subgroup of GL V)—the general linear group on a finite dimensional vector space V. Denote by (Ωm) the space of H1-loops in M starting at a fixed point (m).
For example, we denote by (GL_{n}(R)) the n-dimensional general linear group over (R^{1}) and consider the system x' = f t, x), qquad'=frac{mathrm{d}}{mathrm{d}t}, (1) where (f: R^{1}times R^{n} to R^{n}) is continuous, and for some (Qin GL_{n}(R)), the following affine symmetry holds: f(t+T, x) = Qf bigl t, Q^{-1}x bigr).
Let M n,R) be the set of n×n matrices with real coefficients and let the group G in the above definition be the natural semidirect product Rn⋊G(n), where n≥2 and G(n) is one of the following groups: either the general linear group GL n,R)="{A∈M n,R |det(A)≠0}, or the special linear group SL n,R)="{A∈GL n,R |det(A)="1}, or |SL n,R)|="{A∈GL n,R)||det(A)|="1} or GL+(n,R)="{A∈GL n,R |det(A)>0}.
