For U(N) vector models, primary invariants number f^2 for f≤N and N^2+2N(f−N) for f>N, with secondary invariants appearing and growing as e^{2N log 2 f}.
Poincare series of some pure and mixed trace algebras of two generic matrices
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We work over a field K of characteristic zero. The Poincare series for the algebra C_{n,2} of GL_n-invariants and the algebra T_{n,2} of GL_n-concomitants of two generic n x n matrices x and y are presented for n less than or equal 6. Both simply graded and bigraded cases are included. The cases for n at most 4 were known previously. If n=5 or 6, we show that C_{n,2} has no bigraded system of parameters. For the algebra C_{4,2} and C_{5,2} we construct a minimal set of generators and give an application to Specht's theorem on unitary similarity of two complex matrices. Five conjectures are proposed concerning the numerators and denominators of various Poincare series mentioned above. Some heuristic formulas and open problems are stated.
fields
hep-th 1years
2025 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Bosonic Fortuity in Vector Models
For U(N) vector models, primary invariants number f^2 for f≤N and N^2+2N(f−N) for f>N, with secondary invariants appearing and growing as e^{2N log 2 f}.