Yoga of commutators in DSER elementary orthogonal group
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DOI: 10.1007/s40062-018-0223-5
Abstract: In this article, we consider the Dickson-Siegel-Eichler-Roy (DSER) elementary orthogonal subgroup of the orthogonal group of a non-degenerate quadratic space with a hyperbolic summand over a commutative ring, introduced by Roy. We prove a set… read more here.
Keywords: orthogonal group; elementary orthogonal; group; dser elementary ... See more keywords
Integrable sub-Riemannian geodesic flows on the special orthogonal group
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DOI: 10.1088/1361-6544/ae19c0
Abstract: We analyse the geometry of the rubber-rolling distribution on the special orthogonal group and show that almost all the normal geodesics of any right-invariant sub-Riemannian metric defined on this distribution are completely integrable. Our argument… read more here.
Keywords: integrable sub; special orthogonal; sub riemannian; orthogonal group ... See more keywords
Invariant Rings of the Special Orthogonal Group Have Nonunimodal h-Vectors
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DOI: 10.1142/s0219498825400018
Abstract: For $K$ an infinite field of characteristic other than two, consider the action of the special orthogonal group $\operatorname{SO}_t(K)$ on a polynomial ring via copies of the regular representation. When $K$ has characteristic zero, Boutot's… read more here.
Keywords: rings special; invariant rings; orthogonal group; special orthogonal ... See more keywords
The Hecke algebras for the orthogonal group SO(2,3) and the paramodular group of degree 2
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DOI: 10.1142/s1793042118501464
Abstract: In this paper, we consider the integral orthogonal group with respect to the quadratic form of signature [Formula: see text] given by [Formula: see text] for square-free [Formula: see text]. The associated Hecke algebra is… read more here.
Keywords: orthogonal group; group; see text; formula see ... See more keywords