Gauge invariants and Killing tensors in higher-spin gauge theories

In free completely symmetric tensor gauge field theories on Minkowski space-time, all gauge invariant functions and Killing tensor fields are computed, both on-shell and off-shell. These problems are addressed in the metric-like formalisms.Comment: LaTeX, 24 pages, no figure. One reference added and one definition corrected. Accepted for publication in NP

Invariants, Kronecker Products, and Combinatorics of Some Remarkable Diophantine Systems (Extended Version)

This work lies across three areas (in the title) of investigation that are by themselves of independent interest. A problem that arose in quantum computing led us to a link that tied these areas together. This link consists of a single formal power series with a multifaced interpretation. The deeper exploration of this link yielded results as well as methods for solving some numerical problems in each of these separate areas.Comment: 33 pages, 5 figure

Kronecker Coefficients For Some Near-Rectangular Partitions

We give formulae for computing Kronecker coefficients occurring in the expansion of $s_{\mu}*s_{\nu}$, where both $\mu$ and $\nu$ are nearly rectangular, and have smallest parts equal to either 1 or 2. In particular, we study $s_{(n,n-1,1)}*s_{(n,n)}$, $s_{(n-1,n-1,1)}*s_{(n,n-1)}$, $s_{(n-1,n-1,2)}*s_{(n,n)}$, $s_{(n-1,n-1,1,1)}*s_{(n,n)}$ and $s_{(n,n,1)}*s_{(n,n,1)}$. Our approach relies on the interplay between manipulation of symmetric functions and the representation theory of the symmetric group, mainly employing the Pieri rule and a useful identity of Littlewood. As a consequence of these formulae, we also derive an expression enumerating certain standard Young tableaux of bounded height, in terms of the Motzkin and Catalan numbers

On the growth of the Kronecker coefficients

We study the rate of growth experienced by the Kronecker coefficients as we add cells to the rows and columns indexing partitions. We do this by moving to the setting of the reduced Kronecker coefficients.Comment: Extended version, Containing 4 appendice