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Mikhail Borovoi
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Builings Buildings as generalizainggeneralizations of symmetric spaces

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user267839
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In almost every introductory notes on Tits buildings these are motivated as structures capturing/ sharing several features of symmetric spaces. Could somebody elaborate what are precisely the main structural similarities between buildings and symmetric spaces motivating the vievpoint that buildings can be regarded in some sense as generalizations of symmetric spaces?

(so is there something more 'substantial' beyond the sloppy slogan that both objects carry 'high degree of symmetry'; so what are the 'characteristic' features buildings and symmetric spaces have in common in deeper sense?)

The central construction in the theory of buildings is certain simplicial complex $\Sigma= \Sigma(W,S)$ for appropriate Coxeter group $W$ ( the Weyl group of the buildings) with generators S gouverning the symmetry of the complex. Is there a kind of 'Weyl group' which naturally reflects the symmetry of symmetric spaces?

In almost every introductory notes on Tits buildings these are motivated as structures capturing/ sharing several features of symmetric spaces. Could somebody elaborate what are precisely the main structural similarities between buildings and symmetric spaces motivating the vievpoint that buildings can be regarded in some sense as generalizations of symmetric spaces?

(so is there something more 'substantial' beyond the sloppy slogan that both objects carry 'high degree of symmetry'; so what are the 'characteristic' features buildings and symmetric spaces have in common in deeper sense?)

In almost every introductory notes on Tits buildings these are motivated as structures capturing/ sharing several features of symmetric spaces. Could somebody elaborate what are precisely the main structural similarities between buildings and symmetric spaces motivating the vievpoint that buildings can be regarded in some sense as generalizations of symmetric spaces?

(so is there something more 'substantial' beyond the sloppy slogan that both objects carry 'high degree of symmetry'; so what are the 'characteristic' features buildings and symmetric spaces have in common in deeper sense?)

The central construction in the theory of buildings is certain simplicial complex $\Sigma= \Sigma(W,S)$ for appropriate Coxeter group $W$ ( the Weyl group of the buildings) with generators S gouverning the symmetry of the complex. Is there a kind of 'Weyl group' which naturally reflects the symmetry of symmetric spaces?

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user267839
  • 6k
  • 2
  • 11
  • 42

Builings as generalizaing of symmetric spaces

In almost every introductory notes on Tits buildings these are motivated as structures capturing/ sharing several features of symmetric spaces. Could somebody elaborate what are precisely the main structural similarities between buildings and symmetric spaces motivating the vievpoint that buildings can be regarded in some sense as generalizations of symmetric spaces?

(so is there something more 'substantial' beyond the sloppy slogan that both objects carry 'high degree of symmetry'; so what are the 'characteristic' features buildings and symmetric spaces have in common in deeper sense?)