Symplectic and orthogonal K-groups of the integers
نویسندگان
چکیده
منابع مشابه
Invariant Fields of Symplectic and Orthogonal Groups
The projective orthogonal and symplectic groups POn(F ) and PSpn(F ) have a natural action on the F vector space V ′ = Mn(F ) ⊕ . . . ⊕ Mn(F ). Here we assume F is an infinite field of characteristic not 2. If we assume there is more than one summand in V , then the invariant fields F (V )n and F (V )n are natural objects. They are, for example, the centers of generic algebras with the appropri...
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We consider the action of H = O(p, q) on the matrix space Mp+q,n(R). We study a certain orbit O of H in the null cone N ⊆ Mp+q,n(R) which supports an eigendistribution dνO for H . Using some identities of Capelli type developed in the Appendix, we determine the structure of G̃ = Sp(2n,R)∼-cyclic module generated by dνO under the oscillator representation of G̃ (the metaplectic cover of G = Sp(2n(...
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Formulas for the expansion of arbitrary invariant group functions in terms of the characters for the Sp(2N), SO(2N + 1), and SO(2N) groups are derived using a combinatorial method. The method is similar to one used by Balantekin to expand group functions over the characters of the U(N) group. All three expansions have been checked for all N by using them to calculate the known expansions of the...
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Let G be a finite group and let cd(G) be the set of irreducible ordinary character degrees of G. The degree graph of G is the graph ∆(G) whose set of vertices is the set of primes dividing degrees in cd(G), with an edge between primes p and q if pq divides some degree in cd(G). We determine the graph ∆(G) for the finite simple groups of types B`, C`, D` and D`; that is, for the simple orthogona...
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ژورنال
عنوان ژورنال: Comptes Rendus Mathematique
سال: 2019
ISSN: 1631-073X
DOI: 10.1016/j.crma.2019.08.001