INVARIANT DIFFERENTIAL OPERATORS ON THE MINKOWSKI-EUCLID SPACE

Title & Authors
INVARIANT DIFFERENTIAL OPERATORS ON THE MINKOWSKI-EUCLID SPACE
Yang, Jae-Hyun;

Abstract
For two positive integers $\small{m}$ and $\small{n}$, let $\small{\mathcal{P}_n}$ be the open convex cone in $\small{\mathbb{R}^{n(n+1)/2}}$ consisting of positive definite $\small{n{\times}n}$ real symmetric matrices and let $\small{\mathbb{R}^{(m,n)}}$ be the set of all $\small{m{\times}n}$ real matrices. In this paper, we investigate differential operators on the non-reductive homogeneous space $\small{\mathcal{P}_n{\times}\mathbb{R}^{(m,n)}}$ that are invariant under the natural action of the semidirect product group $\small{GL(n,\mathbb{R}){\times}\mathbb{R}^{(m,n)}}$ on the Minkowski-Euclid space $\small{\mathcal{P}_n{\times}\mathbb{R}^{(m,n)}}$. These invariant differential operators play an important role in the theory of automorphic forms on $\small{GL(n,\mathbb{R}){\times}\mathbb{R}^{(m,n)}}$ generalizing that of automorphic forms on $\small{GL(n,\mathbb{R})}$.
Keywords
invariants;invariant differential operators;the Minkowski-Euclid space;
Language
English
Cited by
1.
POLARIZED REAL TORI,;

대한수학회지, 2015. vol.52. 2, pp.269-331
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