Macdonald formula for spherical functions on affine buildings

A. M. Mantero[1]; A. Zappa[2]

  • [1] D.S.A., Facoltà di Architettura, Università di Genova, St. S. Agostino 37, 16123 Genova, Italy
  • [2] D.I.M.A., Università di Genova, V. Dodecaneso 35, 16146 Genova, Italy

Annales de la faculté des sciences de Toulouse Mathématiques (2011)

  • Volume: 20, Issue: 4, page 669-758
  • ISSN: 0240-2963

Abstract

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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.

How to cite

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Mantero, A. M., and Zappa, A.. "Macdonald formula for spherical functions on affine buildings." Annales de la faculté des sciences de Toulouse Mathématiques 20.4 (2011): 669-758. <http://eudml.org/doc/219771>.

@article{Mantero2011,
abstract = {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.},
affiliation = {D.S.A., Facoltà di Architettura, Università di Genova, St. S. Agostino 37, 16123 Genova, Italy; D.I.M.A., Università di Genova, V. Dodecaneso 35, 16146 Genova, Italy},
author = {Mantero, A. M., Zappa, A.},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {Macdonald spherical functions; affine buildings; Hecke algebra},
language = {eng},
month = {7},
number = {4},
pages = {669-758},
publisher = {Université Paul Sabatier, Toulouse},
title = {Macdonald formula for spherical functions on affine buildings},
url = {http://eudml.org/doc/219771},
volume = {20},
year = {2011},
}

TY - JOUR
AU - Mantero, A. M.
AU - Zappa, A.
TI - Macdonald formula for spherical functions on affine buildings
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2011/7//
PB - Université Paul Sabatier, Toulouse
VL - 20
IS - 4
SP - 669
EP - 758
AB - 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.
LA - eng
KW - Macdonald spherical functions; affine buildings; Hecke algebra
UR - http://eudml.org/doc/219771
ER -

References

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  2. Cartwright (D.I.).— Spherical Harmonic Analysis on Buildings of Type A ˜ n , Monatsh. Math., 133 n. 2: p. 93-109 (2001). Zbl1008.51019MR1860293
  3. Humphreys (J. E.).— Introduction to Lie Algebras and Representation Theory, Graduate Texts in Mathematics, 9, Springer-Verlag, New York-Berlin (1978). Zbl0447.17001MR499562
  4. Humphreys (J. E.).— Reflection Groups and Coxeter Groups, Cambridge Studies in Advanced Mathematics, 29, C.U.P. Cambridge (1990). Zbl0725.20028MR1066460
  5. Macdonald (I. G.).— Spherical Functions on a Group of p-adic type, Publications of the Ramanujan Institute. Ramanujan Institute n. 2, Centre for Advanced Studies in Mathematics, University of Madras, Madras (1971). Zbl0302.43018MR435301
  6. Macdonald (I. G.).— Affine Hecke Algebras and Orthogonal Polynomials, Cambridge Tracts in Mathematics, 157, C.U.P. Cambridge (2003). Zbl1024.33001MR1976581
  7. Mantero (A. M.) and Zappa (A.).— Spherical Functions and Spectrum of the Laplace Operators on Buidings of rank 2, Boll. Un. Mat. Ital. B (7), 8: p. 419-475 (1994). Zbl0815.51010MR1278344
  8. Mantero (A. M.) and Zappa (A.).— Eigenvalues of the vertex set Hecke algebra of an affine building, preprint. Zbl1291.51008
  9. Opdam (E. M.).— On the spectral decomposition of affine Hecke algebras, J. Inst. Math. Jussieu 3 n. 4: p. 531-648 (2007). Zbl1102.22009MR2094450
  10. Parkinson (J.).— Buildings and Hecke Algebras, J. Algebra 297 n. 1, p. 1-49 (2006). Zbl1095.20003MR2206366
  11. Parkinson (J.).— Spherical Harmonic analysis on Affine Buildings, Math. Z. 253 n. 3, p. 571-606 (2006). Zbl1171.43009MR2221087
  12. Ram (A.).— Alcove walks, Hecke algebras, spherical functions, crystal and column strict tableaux, Pure Appl. Math. Q. 2, n. 4, part 2: p. 963-1013 (2006). Zbl1127.20005MR2282411

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