Symplectic tensor invariants, wave graphs and S-tris

TL;DR

This paper introduces symplectic wave graphs and an S-tris game to construct bases for invariants of tensor powers of Sp(2n), extending previous work on SL(n) invariants with novel combinatorial tools.

Contribution

It develops symplectic wave graphs and the S-tris game to explicitly parametrize invariants of Sp(2n), advancing combinatorial methods in tensor invariant theory.

Findings

Bases for invariants parametrized by symplectic wave graphs

Introduction of the S-tris game for proof and construction

Extension of previous SL(n) invariant work to symplectic case

Abstract

The spaces of invariants of tensor powers of the defining representation of Sp(2n) are provided with the bases parametrized by symplectic wave graphs introduced here especially for this purpose. The proof utilizes a game similar to Tetris, named here S-tris. This work continues my previous work on the tensor invariants of SL(n), wave graphs and L-tris.