double coset造句

• The corresponding double coset structure carries information about how the resulting representation decomposes.
• (where is a full set of-double coset representatives, as before ).
• This correspondence identifies with the double coset.
• As noted earlier, in this case the double coset space equals the right coset space.
• Conceptually, this identifies the double coset space with the space of relative configurations of an-coset and a-coset.
• The gluing map ? need only be specified up to taking a double coset in the mapping class group of " H ".
• Assume instead that every-double coset is a finite union of right-cosets and every-double coset is a finite union of left-cosets.
• Assume instead that every-double coset is a finite union of right-cosets and every-double coset is a finite union of left-cosets.
• When the group is a topological group, it is possible to weaken the assumption that the number of left and right cosets in each double coset is finite.
• When a group G has a transitive group action on a set S, computing certain double coset decompositions of G reveals extra information about structure of the action of G on S.
• Note that the cardinality of each double coset must be a multiple of the cardinality of a coset of B . ( And to be honest : it is in fact the quotient that I am interested in ).
• In geometry, a Clifford Klein form is a double coset space, where is a reductive Lie group, is a closed subgroup, and is a discrete subgroup ( of ) that acts properly discontinuously on the homogeneous space.
• The cycle decomposition corresponds to a double coset decomposition G = \ dot { \ cup } _ { j = 1 } ^ t \, \ langle x \ rangle g _ jH of the group G modulo the cyclic group \ langle x \ rangle and modulo the subgroup H.
• In number theory, the Hecke algebra corresponding to a congruence subgroup of the modular group is spanned by elements of the double coset space \ Gamma \ backslash \ mathrm { GL } _ 2 ^ + ( \ mathbb { Q } ) / \ Gamma; the algebra structure is that acquired from the multiplication of double cosets described above.