Tubular Structures of Compact Symmetric Spaces Associated with the Exceptional Lie Group F4

2004 ◽  
Vol 109 (1) ◽  
pp. 239-252
Author(s):  
Balázs Csikós ◽  
László Verhóczki
Keyword(s):  
Lie Group ◽  
Symmetric Spaces ◽  
Tubular Structures ◽  
Compact Symmetric Spaces

scholarly journals Integral geometry under cut loci in compact symmetric spaces

1995 ◽  
Vol 137 ◽  
pp. 33-53 ◽  
Author(s):  
Hiroyuki Tasaki
Keyword(s):  
Invariant Measure ◽  
Lie Group ◽  
Integral Geometry ◽  
Symmetric Spaces ◽  
Homogeneous Spaces ◽  
Integral Invariant ◽  
Identity Component ◽  
Integral Invariants ◽  
Compact Symmetric Spaces ◽  
Group Of Isometries

The theory of integral geometry has mainly treated identities between integral invariants of submanifolds in Riemannian homogeneous spaces like as dμg(g) where M and N are submanifolds in a Riemannian homogeneous spaces of a Lie group G and I(M ∩ gN) is an integral invariant of M ∩ gN. For example Poincaré’s formula is one of typical identities in integral geometry, which is as follows. We denote by M(R2) the identity component of the group of isometries of the plane R2 with a suitable invariant measure μM(R2).

scholarly journals Approximate Formulas for Zeta Functions of Selberg’s Type in Quotients of SL4

2020 ◽  
Vol 14 ◽  
Keyword(s):  
Lie Group ◽  
Symmetric Spaces ◽  
Logarithmic Derivative ◽  
Zeta Functions ◽  
Locally Symmetric Spaces ◽  
Compact Symmetric Spaces ◽  
Approximate Formulas

The goal of the paper is to derive some approximate formulas for the logarithmic derivative of several zata functions of Selberg’s type for compact symmetric spaces formed as quotients of the Lie group SL4 (R). Such formulas, known in literature as Tutchmarsh-Landau style approximate formulas, are usually applied in order to obtain prime geodesic theorems in various settings of underlying locally symmetric spaces.

scholarly journals On some recent progress in the classification of $$(P\hbox { and }Q)$$-polynomial association schemes

2019 ◽  
Author(s):  
Alexander L. Gavrilyuk ◽  
Jack H. Koolen
Keyword(s):  
Symmetric Spaces ◽  
Recent Progress ◽  
Association Schemes ◽  
Compact Symmetric Spaces ◽  
Expository Paper

AbstractThe problem of classification of $$(P\hbox { and }Q)$$(PandQ)-polynomial association schemes, as a finite analogue of E. Cartan’s classification of compact symmetric spaces, was posed in the monograph “Association schemes” by E. Bannai and T. Ito in the early 1980s. In this expository paper, we report on some recent results towards its solution.

Corwin–Greenleaf multiplicity functions for complex semisimple symmetric spaces

2015 ◽  
Vol 26 (05) ◽  
pp. 1550039
Author(s):  
Salma Nasrin
Keyword(s):  
Symmetric Space ◽  
Lie Algebras ◽  
Lie Group ◽  
Symmetric Spaces ◽  
Coadjoint Orbit ◽  
Natural Projection ◽  
Real Form ◽  
Single Orbit ◽  
Complex Semisimple ◽  
Complex Symmetric

Let Gℂ be a complex simple Lie group, GU a compact real form, and [Formula: see text] the natural projection between the dual of the Lie algebras. We prove that, for any coadjoint orbit [Formula: see text] of GU, the intersection of [Formula: see text] with a coadjoint orbit [Formula: see text] of Gℂ is either an empty set or a single orbit of GU if [Formula: see text] is isomorphic to a complex symmetric space.

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