scholarly journals A Maximal Operator and a Covering Lemma on Non-Compact Symmetric Spaces

2000 ◽  
Vol 7 (1) ◽  
pp. 83-93 ◽  
Author(s):  
Alexandru D. Ionescu
Keyword(s):  
Maximal Operator ◽  
Symmetric Spaces ◽  
Covering Lemma ◽  
Compact 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.

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).

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