English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

A filtration of a representation whose successive quotients are isomorphic toDemazure modules is called an excellent filtration. In this paper we studygraded multiplicities in excellent filtrations of fusion products for thecurrent algebra $\mathfrak{sl}_2[t]$. We give a combinatorial formula for thepolynomials encoding these multiplicities in terms of two dimensional latticepaths. Corollaries to our main theorem include a combinatorial interpretationof various objects such as the coeffficients of Ramanujan's fifth order mocktheta functions $\phi_0, \phi_1, \psi_0, \psi_1$, Kostka polynomials for hookpartitions and quotients of Chebyshev polynomials. We also get a combinatorialinterpretation of the graded multiplicities in a level one flag of a local Weylmodule associated to the simple Lie algebras of type $B_n \text{ and } G_2$.

A combinatorial formula for graded multiplicities in excellent filtrations