Abstract
Several constructions of Laplace operators for the canonical realization of the orthogonal Lie algebra are discussed. All of them are related with the Capelli-type determinant of a matrix formed by the generators of this Lie algebra. Combinatorial properties of the projection map S N → S N − 1 used in the definition of the Capelli-type determinant are studied. It is proved that the fibers of this projection form a partition of the Bruhat order on S N into Boolean intervals such that the number of intervals with 2 k elements is the Stirling number of the first kind c( N − 1, k).
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
