Tag Archives: matrix groups

Polynomials and Representations XXXIII

Posted on June 23, 2016 by limsup

We are back to the convention and We wish to focus on irreducible polynomial representations of G. The weak Peter-Weyl 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 →

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Polynomials and Representations XXXII

Posted on June 21, 2016 by limsup

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. Peter-Weyl Principle: any irrep can be embedded inside … Continue reading →

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Polynomials and Representations XXXI

Posted on June 19, 2016 by limsup

K-Representations and G-Representations 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 →

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