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Tag Archives: matrix groups
Polynomials and Representations XXXIII
We are back to the convention and We wish to focus on irreducible polynomial representations of G. The weak PeterWeyl theorem gives: Theorem. Restricting the RHS to only polynomial irreducible V gives us on the LHS, where each polynomial in restricts to a function … Continue reading
Polynomials and Representations XXXII
We attempt to identify the irreducible rational representations of From the last article, we may tensor it with a suitable power of det and assume it is polynomial. One key ingredient is the following rather ambiguous statement. PeterWeyl Principle: any irrep can be embedded inside … Continue reading
Polynomials and Representations XXXI
KRepresentations and GRepresentations As mentioned at the end of the previous article, we shall attempt to construct analytic representations of from continuous representations of Let . Consider , where is the group of diagonal matrices in K so as a topological group. From our … Continue reading