Stirling partitions of the symmetric group and Laplace operators for the orthogonal Lie algebra
type: Item
instance of: scholarly article
title: Stirling partitions of the symmetric group and Laplace operators for the orthogonal Lie algebra
zbMATH Open document ID: 0895.05006
DOI: 10.1016/S0012-365X(97)00120-9
author: Alexander Molev
published in: Discrete Mathematics
publication date: 1998-06-02T00:00:00Z
review text: If \(S_N\) and \(S_{N-1}\) are symmetric groups equipped with the Bruhat order, then the standard inclusion \(i_N\colon S_{N-1}\to S_N\) is well-behaved as a mapping of posets. On the other hand projections \(\pi_N\colon S_N\to S_{N-1}\) need to be defined with more care if \(i_N\circ \pi_N\) is to be the identity map as well as order-preserving. Accordingly, the author defines a particular such projection and uses its inverse to partition \(S_N\) into Boolean (algebra) intervals \(B_k\), generating Stirling partitions if the number of intervals \(B_k\) is the (signless) Stirling number (of the first kind). From the combinatorial properties he is then able to provide descriptive information concerning generalized determinants and related forms on certain Lie and enveloping algebras, thereby giving a combinatorial perspective as developed by the author and others in a considerable sequence of previous papers along with the present one in mathematical journals as well as journals of physics.
reviewed by: J. Neggers
Mathematics Subject Classification ID: 05E10
Mathematics Subject Classification ID: 05A18
Mathematics Subject Classification ID: 17B05
zbMATH DE Number: 1135944
zbMATH Keywords: Laplace operators
zbMATH Keywords: symmetric groups
zbMATH Keywords: Bruhat order
zbMATH Keywords: posets
zbMATH Keywords: Stirling partitions
zbMATH Keywords: Stirling number
zbMATH Keywords: generalized determinants
zbMATH Keywords: Lie and enveloping algebras
MaRDI profile type: Publication
Wikidata QID: Q115340637
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description: scientific article; zbMATH DE number 1135944