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Counting Borel Orbits in Symmetric Spaces of Types BI and CII

Counting Borel Orbits in Symmetric Spaces of Types BI and CII This is a continuation of our combinatorial program on the enumeration of Borel orbits in symmetric spaces of classical types. Here, we determine the generating series the numbers of Borel orbits in $${\mathbf {SO}}_{2n+1}/{\mathbf {S(O}}_{2p}\times {\mathbf {O}}_{2q+1} \mathbf {)}$$ SO 2 n + 1 / S ( O 2 p × O 2 q + 1 ) (type BI) and in $${\mathbf {Sp}}_n/{\mathbf {Sp}}_p \times {\mathbf {Sp}}_q$$ Sp n / Sp p × Sp q (type CII). In addition, we explore relations to lattice path enumeration. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Arnold Mathematical Journal Springer Journals

Counting Borel Orbits in Symmetric Spaces of Types BI and CII

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References (10)

Publisher
Springer Journals
Copyright
Copyright © 2018 by Institute for Mathematical Sciences (IMS), Stony Brook University, NY
Subject
Mathematics; Mathematics, general
ISSN
2199-6792
eISSN
2199-6806
DOI
10.1007/s40598-018-0092-3
Publisher site
See Article on Publisher Site

Abstract

This is a continuation of our combinatorial program on the enumeration of Borel orbits in symmetric spaces of classical types. Here, we determine the generating series the numbers of Borel orbits in $${\mathbf {SO}}_{2n+1}/{\mathbf {S(O}}_{2p}\times {\mathbf {O}}_{2q+1} \mathbf {)}$$ SO 2 n + 1 / S ( O 2 p × O 2 q + 1 ) (type BI) and in $${\mathbf {Sp}}_n/{\mathbf {Sp}}_p \times {\mathbf {Sp}}_q$$ Sp n / Sp p × Sp q (type CII). In addition, we explore relations to lattice path enumeration.

Journal

Arnold Mathematical Journal – Springer Journals

Published: Sep 10, 2018

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