Papers › On Kostant's weight q-multiplicity formula for 𝔰𝔭₆(ℂ)

On Kostant's weight q-multiplicity formula for 𝔰𝔭₆(ℂ)

16 Aug 2021arXiv:2108.07217links table onlyarchive 2025-07-28

Pamela E. Harris, Peter Hollander, Daniel C. Qin, Maria Rodriguez-Hertz

The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.

Kostant's weight q-multiplicity formula is an alternating sum over a finite group known as the Weyl group, whose terms involve the q-analog of Kostant's partition function. The q-analog of the partition function is a polynomial-valued function defined by ℘_q(ξ)=∑ᵢ₌₀ᵏ cᵢ qⁱ, where cᵢ is the number of ways the weight ξ can be written as a sum of exactly i positive roots of a Lie algebra 𝔤. The evaluation of the q-multiplicity formula at q = 1 recovers the multiplicity of a weight in an irreducible highest weight representation of 𝔤. In this paper, we specialize to the Lie algebra 𝔰𝔭₆(ℂ) and we provide a closed formula for the q-analog of Kostant's partition function, which extends recent results of Shahi, Refaghat, and Marefat. We also describe the supporting sets of the multiplicity formula (known as the Weyl alternation sets of 𝔰𝔭₆(ℂ)), and use these results to provide a closed formula for the q-multiplicity for any pair of dominant integral weights of 𝔰𝔭₆(ℂ). Throughout this work, we provide code to facilitate these computations.

Code

Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.

Code Syntology ran Syntology

Not run by Syntology. Nothing on this page verifies that the listed code works.

Results from the paper archive 2025-07-28

No leaderboard rows for this paper in the archive.

Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections