| Abstract: |
The construction of bases of multi-matrix invariants has applications to many systems with matrix degrees of freedom, including matrix models, gauged matrix quantum mechanics, \mathcal{N}=4 SYM and the AdS/CFT correspondence. In the large-N limit, such invariants are efficiently described using multi-trace structures. At finite N, however, the space of invariants is truncated due to non-trivial trace relations, necessitating more sophisticated tools. Two well-known orthogonal bases that accommodate finite-N effects are the restricted Schur and covariant bases. Their construction relies on representation theoretic data: Young diagrams, multiplicity labels, and branching or Clebsch–Gordan coefficients for symmetric groups. Computing these coefficients is, in general, technically challenging. In this talk, I will present an algebraic method for constructing orthogonal bases at finite N, which avoids the explicit computation of branching and Clebsch-Gordan coefficients. I will focus on the two-matrix case, which is directly relevant to the construction of 1/4 BPS operators in \mathcal{N}=4 SYM. |
