skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


  • Home
  • Search Results
  • Page 1 of 1

Search for: All records

Award ID contains: 1717543

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. ; ; ; (, The American Mathematical Monthly)
    Full Text Available 
  2. ; ; (, The Australasian journal of combinatorics)
    For a given weight of a complex simple Lie algebra, the q-analog of Kostant’s partition function is a polynomial valued function in the variable q, where the coefficient of qk is the number of ways the weight can be written as a nonnegative integral sum of exactly k positive roots. In this paper we determine generating functions for the q-analog of Kostant’s partition function when the weight in question is the highest root of the classical Lie algebras of types B, C, and D, and the exceptional Lie algebras of type G2, F4, E6, E7, and E8. 
    more » « less
    Accepted Manuscript Full Text Available
  3. ; ; (, Applicable Algebra in Engineering, Communication and Computing)
    The multiplicity of a weight μμ in an irreducible representation of a simple Lie algebra gg with highest weight λλ can be computed via the use of Kostant’s weight multiplicity formula. This formula is an alternating sum over the Weyl group and involves the computation of a partition function. In this paper we consider a q-analog of Kostant’s weight multiplicity and present a SageMath program to compute q-multiplicities for the simple Lie algebras. 
    more » « less
    Full Text Available 
  4. ; ; ; (, Journal of Combinatorial Theory, Series A)
    Full Text Available 
  5. (, Notices of the American Mathematical Society)
    Full Text Available