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m -parallelisms.

Johnson, Norman L., Pomareda, Rolando (2002)

International Journal of Mathematics and Mathematical Sciences

Macdonald formula for spherical functions on affine buildings

A. M. Mantero, A. Zappa (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

In this paper we explicitly determine the Macdonald formula for spherical functions on any locally finite, regular and affine Bruhat-Tits building, by constructing the finite difference equations that must be satisfied and explaining how they arise, by only using the geometric properties of the building.

Minimal length coset representatives for quotients of parabolic subgroups in Coxeter groups

Fabio Stumbo (2000)

Bollettino dell'Unione Matematica Italiana

In questo lavoro viene trovata un'espressione esplicita per i rappresentanti dei laterali di sottogrupi parabolici di gruppi di Coxeter aventi lunghezza minima: dato un sistema di Coxeter W , S ed un suo sottogruppo parabolico W I , I , con I S , si determina esplicitamente in ogni laterale W I w di W I un elemento avente lunghezza minima. Nella sezione 2 trattiamo i casi classici, i.e. W = A n , B n e D n . Dopo ciò, nella sezione 3, diamo una procedura per risolvere il problema nei restanti casi eccezionali, insieme a qualche...

Modular lattices from finite projective planes

Tathagata Basak (2014)

Journal de Théorie des Nombres de Bordeaux

Using the geometry of the projective plane over the finite field 𝔽 q , we construct a Hermitian Lorentzian lattice L q of dimension ( q 2 + q + 2 ) defined over a certain number ring 𝒪 that depends on q . We show that infinitely many of these lattices are p -modular, that is, p L q ' = L q , where p is some prime in 𝒪 such that | p | 2 = q .The Lorentzian lattices L q sometimes lead to construction of interesting positive definite lattices. In particular, if q 3 mod 4 is a rational prime such that ( q 2 + q + 1 ) is norm of some element in [ - q ] , then we find a 2 q ( q + 1 ) dimensional...

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