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Congruences of shifted Jack Littlewood-Richardson coefficients
Ryan Mickler
The shifted Jack Littlewood-Richardson coefficients generalize the ordinary Jack coefficients and are Laurent polynomials in the Jack parameter . We prove a previously conjectur…
Hidden Structure of Jack Littlewood-Richardson Coefficients
Ryan Mickler
We argue that Jack Littlewood-Richardson coefficients are specialisations of certain novel polynomials. For the triple of partitions , we prove t…
The Stanley Conjecture Revisited
Ryan Mickler
In the seminal work of Stanley, several conjectures were made on the structure of Littlewood-Richardson coefficients for the multiplication of Jack symmetric functions. Motivated b…
New cases of the Strong Stanley Conjecture
Per Alexandersson, Ryan Mickler
We make progress towards understanding the structure of Littlewood-Richardson coefficients for products of Jack symmetric functions. Building on recent results of the s…
Jack Littlewood-Richardson Coefficients and the Nazarov-Sklyanin Lax Operator
Ryan Mickler
We continue the work begun by Mickler-Moll investigating the properties of the polynomial eigenfunctions of the Nazarov-Sklyanin quantum Lax operator. By considering products of th…
Spectral Theory of the Nazarov-Sklyanin Lax Operator
Ryan Mickler, Alexander Moll
In their study of Jack polynomials, Nazarov-Sklyanin introduced a remarkable new graded linear operator where is the ring of symmetr…