| Abstrakt: |
Let K be the product ... of orthogonal groups. Let V = ⊗i=1r ..., the r-fold tensor product of defining representations of each orthogonal factor. We compute a stable formula for the dimension of the K-invariant algebra of degree d homogeneous polynomial functions on V . To accomplish this, we compute a formula for the number of matchings which commute with a fixed permutation. Finally, we provide formulas for the invariants and describe a bijection between a basis for the space of invariants and the isomorphism classes of certain r-regular graphs on d vertices, as well as a method of associating each invariant to other combinatorial settings such as phylogenetic trees. [ABSTRACT FROM AUTHOR] |
