In group theory, a field of mathematics, a double coset is a collection of group elements which are equivalent under the symmetries coming from two subgroups, generalizing the notion of a single coset.[1][2]
^Hall, Jr., Marshall (1959), The Theory of Groups, New York: Macmillan, pp. 14–15
^Bechtell, Homer (1971), The Theory of Groups, Addison-Wesley, p. 101
set of G into disjoint, equal-size subsets called cosets. There are left cosets and right cosets. Cosets (both left and right) have the same number of elements...
In group theory, a field of mathematics, a doublecoset is a collection of group elements which are equivalent under the symmetries coming from two subgroups...
correspond to the left cosets G/Ho, and the marked point o corresponds to the coset of the identity. Conversely, given a coset space G/H, it is a homogeneous...
_{t^{-1}Ht\cap K}\right\rangle ,\end{aligned}}} (where T is a full set of (H, K)-doublecoset representatives, as before). This formula is often used when θ and ψ...
{\displaystyle L^{1}(G//K)} where G / / K {\displaystyle G//K} is the doublecoset space of S L ( 2 , R ) {\displaystyle SL(2,\mathbb {R} )} (see Zonal...
union of doublecosets of B parameterized by the elements of the Weyl group W. (Note that although W is not in general a subgroup of G, the coset wB is still...
operators is by means of doublecosets in the modular group. In the contemporary adelic approach, this translates to doublecosets with respect to some compact...
at most finitely many doublecoset classes HaK in F(X) such that H ∩ aKa−1 ≠ {1}. Suppose that at least one such doublecoset exists and let a1,...,an...
up to isotopy. The gluing map ƒ need only be specified up to taking a doublecoset in the mapping class group of H. This connection with the mapping class...
(of subsets) and multiplication as product of subsets. Central product Doublecoset Adolfo Ballester-Bolinches; Ramon Esteban-Romero; Mohamed Asaad (2010)...
torsion-free uniform subgroup of G and M can then be identified with the doublecoset space Γ \ G / K. In the case of the sphere and the Euclidean plane, the...
For every sufficiently small compact open subgroup K of G(Aƒ), the doublecoset space Sh K ( G , X ) = G ( Q ) ∖ X × G ( A f ) / K {\displaystyle \operatorname...
group the simplest definition is, roughly speaking, that the (K,K )-doublecosets in G commute. More precisely, the Hecke algebra, the algebra of functions...
The Hecke algebra of a finite group is the algebra spanned by the doublecosets HgH of a subgroup H of a finite group G. It is a special case of a Hecke...
set difference. The backslash is also sometimes used to denote the right coset space. Especially when describing computer algorithms, it is common to define...
group and K is any subgroup of G, then the Hecke algebra is spanned by doublecosets of H\G/H. For the special linear group over the p-adic numbers, G =...
The Bruhat decomposition G = BWB of a semisimple algebraic group into doublecosets of a Borel subgroup can be regarded as a generalization of the principle...
{\displaystyle g} , T g {\displaystyle {\mathcal {T}}_{g}} , as the Doublecoset space T g ≅ G L Z ( 2 g ) ∖ G L R ( 2 g ) / G L C ( g ) {\displaystyle...
(2,k)=\mathbf {B} \cup \mathbf {B} \cdot J\cdot \mathbf {B} ,}} the doublecoset decomposition of SL(2,k). In fact the union is disjoint and can be written...
of the Sylow Theorems (replacing an older cumbersome proof involving doublecosets) that is in the standard textbooks on Abstract Algebra, i.e. Group Theory...
Springer-Verlag, p. 17 Jones, Andrew R. (1996), "A Combinatorial Approach to the DoubleCosets of the Symmetric Group with respect to Young Subgroups", Europ. J. Combinatorics...
{\begin{pmatrix}0&1\\-1&0\end{pmatrix}}} . Then, as is easily verified, the doublecoset BsB is dense in G; this is a special case of the Bruhat decomposition...
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