"Kostant partition function"의 두 판 사이의 차이

2016년 6월 30일 (목) 19:23 판

Kostant’s partition function counts the number of ways to represent a particular vector (weight) as a nonnegative integral sum of positive roots of a Lie algebra.
For a given weight the q-analog of Kostant’s partition function is a polynomial where the coefficient of $q^k$ is the number of ways the weight can be written as a nonnegative integral sum of exactly $k$ positive roots.

Kostant’s partition function was introduced and studied by F.A. Berezin and I.M. Gelfand (Proc. Moscow Math. Soc. 5 (1956), 311-351) for the case $g=sl(n)$, and by B. Kostant (Trans. Amer. Math. Soc., 93 (1959), 53-73) for arbitrary semi–simple finite dimensional Lie algebra $g$

Flow polytopes and the Kostant partition function
Harris, Pamela E., Erik Insko, and Mohamed Omar. “The $q$-Analog of Kostant’s Partition Function and the Highest Root of the Classical Lie Algebras.” arXiv:1508.07934 [math], August 31, 2015. http://arxiv.org/abs/1508.07934.

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+==introduction==
+* Kostant’s  partition  function  counts  the  number  of  ways  to  represent  a  particular  vector (weight) as a nonnegative integral sum of positive roots of a Lie algebra.
+* For a given weight the q-analog of Kostant’s partition function is a polynomial where the coefficient of $q^k$ is the number of ways the weight can be written as a nonnegative integral sum of exactly $k$ positive roots.
+==history==
+* Kostant’s partition function was introduced and studied by F.A. Berezin and I.M. Gelfand (Proc. Moscow Math. Soc. 5 (1956), 311-351) for the case $g=sl(n)$, and by B. Kostant (Trans. Amer. Math. Soc., 93 (1959), 53-73) for arbitrary semi–simple finite dimensional Lie algebra $g$
 ==articles==
 * [http://www-math.mit.edu/~karola/ Flow polytopes and the Kostant partition function]