Abstract
In this thesis, we consider some aspects of noncommutative classical invariant theory, i.e., noncommutative invariants of the classical group SL(2, k). We develop a symbolic method for invariants and covariants, and we use the method to compute some invariant algebras. The subspace Ĩ ${}_{d}^{m}$ of the noncommutative invariant algebra Ĩd consisting of homogeneous elements of degree m has the structure of a module over the symmetric group Sm. We find the explicit decomposition into irreducible modules. As a consequence, we obtain the Hilbert series of the commutative classical invariant algebras. The Cayley—Sylvester theorem and the Hermite reciprocity law are studied in some detail. We consider a new power series H(Ĩd, t) whose coefficients are the number of irreducible Sm-modules in the decomposition of Ĩ ${}_{d}^{m}$ , and show that it is rational. Finally, we develop some analogues of all this for covariants.
Citation
Torbjörn Tambour. "Noncommutative classical invariant theory." Ark. Mat. 29 (1-2) 127 - 182, 1991. https://doi.org/10.1007/BF02384335
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