International Journal of Nonlinear Analysis and Applications

The q-analog of Kostant's partition function for $\mathfrak{sl_\textrm{4}(\mathbb{C})} $ and $\mathfrak{sp_\textrm{6}(\mathbb{C})}$

Document Type : Special issue editorial

Authors

1 Department of Mathematics, Tabriz Branch, Islamic Azad University Tabriz, Iran

2 Department of Mathematics, Shabestar Branch, Islamic Azad University, Shabestar, Iran

Abstract

In this paper, we consider the q-analog of Kostant's Partition Function of Lie algebras  $\mathfrak{sl_\textrm{4}(\mathbb{C})} $ and $\mathfrak{sp_\textrm{6}(\mathbb{C})}$ and present a closed formula for the values of these functions.

Keywords

[1] R.W. Carter, Lie algebras of finite and affine type, Cambridge University Press, 2005.
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[3] P.E. Harris and E.L. Lauber, Weight q-multiplicities for Representations of sp4(C), J. Siber. Federal Univ. Math. Phys. 10 (2017), no. 4, 494–502.
[4] B. Kostant, A formula for the multiplicity of a weight, Proc. Natl. Acad. Sci. USA 44 (1958), no. 6, 588–589.
[5] G. Lusztig, Singularities character formulas and a q-analog of weight multiplicities, Asterisque 101 (1983), no. 102, 208–229.
[6] H. Refaghat and M. Shahryari, Kostant partition function for sp4(C), J. Siber. Federal Univ. Math. Phys. 5 (2012), no. 1, 18–24.
[7] E. Shahi, H. Refaghat and Y. Marefat, Kostant’s partition function for the Lie algebras sl4(C) and sp6(C), RMS: Res. Math. Statist. 8 (2021), no. 1, 1–6.
International Journal of Nonlinear Analysis and Applications
Volume 15, Issue 3
March 2024
Pages 305-314
  • Receive Date: 07 September 2022
  • Revise Date: 02 December 2022
  • Accept Date: 15 December 2022