Algebraic Structure
It is possible to define a product operation of double cosets in an associated ring.
Given two double cosets and, we decompose each into right cosets and . If we write, then we can define the product of with as the formal sum
An important case is when H = K = L, which allows us to define an algebra structure on the associated ring spanned by linear combinations of double cosets.
Read more about this topic: Double Coset
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