We establish a strong connection between buildings and Hecke algebras through the study of two algebras of averaging operators on buildings. To each locally finite regular building we associate a natural algebra B of chamber set averaging operators, and when the building is affine we also define an algebra A of vertex set averaging operators. In the affine case, it is shown how the building gives rise to a combinatorial and geometric description of the Macdonald spherical functions, and of the centers of affine Hecke algebras. The algebra homomorphisms from A into the complex numbers are studied, and some associated spherical harmonic analysis is conducted. This generalises known results concerning spherical functions on groups of p-adic type. As an application of this spherical harmonic analysis we prove a local limit theorem for radial random walks on affine buildings.

Thesis (M.A.)--Trinity Evangelical Divinity School, 1995. / Abstract. Includes bibliographical references (leaves 90-93).

Dissertação (mestrado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Matemática, 2013. / Submitted by Luiza Silva Almeida (luizaalmeida@bce.unb.br) on 2013-07-16T16:36:56Z No. of bitstreams: 1 2013_OttoAugustodeMoraisCosta.pdf: 643449 bytes, checksum: 5c1dc30e495fb393e98796175549d80d (MD5) / Approved for entry into archive by Leandro Silva Borges(leandroborges@bce.unb.br) on 2013-07-16T20:28:44Z (GMT) No. of bitstreams: 1 2013_OttoAugustodeMoraisCosta.pdf: 643449 bytes, checksum: 5c1dc30e495fb393e98796175549d80d (MD5) / Made available in DSpace on 2013-07-16T20:28:44Z (GMT). No. of bitstreams: 1 2013_OttoAugustodeMoraisCosta.pdf: 643449 bytes, checksum: 5c1dc30e495fb393e98796175549d80d (MD5) / Neste trabalho, fazemos um breve estudo a respeito dos grupos de reflexões finitos, para os quais associamos sistemas de raízes, matrizes de Cartan e grafos, a fim de classificarmos todos os tais grupos. Em seguida, estudamos uma generalização desses grupos para os denominados grupos de Coxeter. Utilizando a função comprimento como ferramenta fundamental, mencionamos diversos resultados acerca dos subgrupos parabólicos. No último capítulo, determinamos a estrutura dos centralizadores dos elementos de um grupo de Coxeter finito, seguindo o artigo: M. Konvalinka, G. Pfeiffer, C.E. Röver, ‘A note on element centralizers in finite Coxeter groups', J. Group Theory, 14 (2011) 727-745. Como aplicação final, apresentamos uma demonstração alternativa de um importante teorema de Solomon, conhecido como a fórmula de Solomon. _______________________________________________________________________________________ ABSTRACT / This work is a brief study about the finite reflections groups, to which we associate root systems, Cartan matrices and Coxeter graphs, in order to classicate such groups. After that, we study a generalisation of these groups to Coxeter groups. By using the lenght function as fundamental tool, we mention various results about the parabolic subgroups. In the last chapter we determinate the structure of the element centralisers of a finite Coxeter group, following the paper: M. Konvalinka, G. Pfeiffer, C.E. Röver, ‘A note on element centralizers in finite Coxeter groups', J. Group Theory, 14 (2011) 727-745. As final application we present an alternative proof of an important theorem of Solomon, known as the Solomon formula.

L’accès à la justice est considéré comme un des principaux problèmes du milieu juridique canadien depuis plus de trente ans et a acquis une place d’importance dans le discours juridique, notamment en matière de droits de la personne. En effet, à la suite de l’arrêt Ménard c. Rivet qui est venu restreindre de façon considérable l’accès des citoyens au Tribunal des droits de la personne, plusieurs auteurs se sont prononcés sur la question de l’accès à la justice en matière de droits de la personne. L’étude des discours juridiques permet de constater que la plupart d’entre eux traitent des aspects de l’accès à la justice relatifs à l’accès aux tribunaux ou aux institutions. Cependant, il semble que la société pluraliste dans laquelle nous vivons commande d’élargir la notion d’accès à la justice. Roderick A. Macdonald partage une telle conceptualisation de l’accès à la justice. Prenant appui sur le modèle de pensée du professeur Macdonald, il sera possible d’éclairer les fondements des discours juridiques portant sur l’accès à la justice afin de saisir les différents sens que peut prendre l’accès à la justice et d’envisager une transformation du discours sur l’accès à la justice en matière de droits de la personne. De façon plus concrète, cette étude sur l’accès à la justice s’intéresse à un problème fondamental du système judiciaire et à la recherche de solutions qui permettront de redonner confiance aux citoyens en l’administration de la justice.

No description available.

No description available.

George MacDonald's novel Lilith relates the story of a young man inheriting his deceased father's estate and coming in contact with its remarkable library and mysterious librarian. The protagonist's subsequent adventures in a fantastical world prepare the young Mr. Vane to assume authority over his inherited archive and become an archon. Jacques Derrida's exposition of the responsibilities of the archon including archival authority, domiciliation, and consignation illuminate the mentoring role of the elusive librarian Mr. Raven in Vane's adventures. By using Derrida's deconstruction of archives to unpack the intricacies of knowledge transfer in MacDonald's novel, the lasting impact of the archon on the archive and the individuals in Lilith, as well as the importance of the archon in the transfer of knowledge between individuals facilitated through relationships, becomes apparent. The archon, acting as a gatherer, organizer, and shaper of texts, uses the materials within the archive to exercise power and to bequeath power upon other individuals, as seen in the character Mr. Raven's actions. Lilith illustrates the necessity of the archon as he shapes the archive's contents and governs the interactions between book and reader, ultimately allowing the archive to become a place where knowledge is heritable.

No description available.

No description available.

No description available.