Welcome to Maarten Solleveld's homepage

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Here you can download my papers and thesis as pdf-files.
They are grouped according to topic (although in several cases there is substantial overlap).
Summaries can be found on the arXiv.



Local Langlands program

 Affine Hecke algebras for classical p-adic groups
    joint with Anne-Marie Aubert and Ahmed Moussaoui
    preprint, arXiv:2211.08196, November 2022

 Affine Hecke algebras for Langlands parameters
    joint with Anne-Marie Aubert and Ahmed Moussaoui
    preprint, arXiv:1701.03593, December 2019

 Langlands parameters, functoriality and Hecke algebras
    Pacific Journal of Mathematics 304.1 (2020), 209-302

 Generalizations of the Springer correspondence and cuspidal Langlands parameters
    joint with Anne-Marie Aubert and Ahmed Moussaoui
    Manuscripta Mathematica 157 (2018), 121-192

 Conjectures about p-adic groups and their noncommutative geometry
    joint with Anne-Marie Aubert, Paul Baum and Roger Plymen
    Contemporary Mathematics 691 (2017), 15-51

 On the local Langlands correspondence for non-tempered representations
    joint with Anne-Marie Aubert, Paul Baum and Roger Plymen
    Münster Journal of Mathematics 7 (2014) 27-50


Unipotent representations

 On unipotent representations of ramified p-adic groups
    Representation Theory 27 (2023), 669--716

 On formal degrees of unipotent representations
    joint with Yongqi Feng and Eric Opdam
    J. Inst. Math. Jussieu 21.6 (2022), 1947--1999

 A local Langlands correspondence for unipotent representations
    American Journal of Mathematics 145.3 (2023), 673--719

 Supercuspidal unipotent representations: L-packets and formal degrees
    joint with Yongqi Feng and Eric Opdam
    Journal de l'École polytechnique Mathématiques 7 (2020), 1133-1193


GLn, SLn, and their inner forms

  Smooth duals of inner forms of GLn and SLn
    joint with Anne-Marie Aubert, Paul Baum and Roger Plymen
    Documenta Mathematica 24 (2019), 373-420

  On L-packets and depth for SL2(K) and its inner form
    joint with Anne-Marie Aubert, Sergio Mendes and Roger Plymen
    International Journal of Number Theory 10.13 (2017), 2545-2568

 Hecke algebras for inner forms of p-adic special linear groups
    joint with Anne-Marie Aubert, Paul Baum and Roger Plymen
    Journal de l'Institut de Mathématiques de Jussieu 16.2 (2017), 351-419

 Depth and the local Langlands correspondence
    joint with Anne-Marie Aubert, Paul Baum and Roger Plymen
    pp. 17--41 in: Arbeitstagung Bonn 2013. In memory of Friedrich Hirzebruch
    Progress in Mathematics 319, Birkhäuser, 2016

 The local Langlands correspondence for inner forms of SLn
    joint with Anne-Marie Aubert, Paul Baum and Roger Plymen
    Research in the Mathematical Sciences 3.32 (2016)


Principal series representations

 On principal series representations of quasi-split reductive p-adic groups
    preprint, arXiv:2304.06418, April 2023

 The principal series of p-adic groups with disconnected centre
    joint with Anne-Marie Aubert, Paul Baum and Roger Plymen
    Proceedings London Mathematical Society 114.5 (2017), 798-854

 Geometric structure for the principal series of a split reductive p-adic group with connected centre
    joint with Anne-Marie Aubert, Paul Baum and Roger Plymen
    Journal of Noncommutative Geometry 10 (2016), 663-680

 Geometric structure and the local Langlands conjecture
    joint with Anne-Marie Aubert, Paul Baum and Roger Plymen
    preprint, arXiv:1211.0180v3, 2013

p-adic groups and their buildings

 The Buildings Gallery: visualising buildings
    joint with Bram Bekker
    Journal of Mathematics and the Arts 16 (2022), doi.org/10.1080/17513472.2022.2063782

 Pseudo-reductive and quasi-reductive groups over non-archimedean local fields
    Journal of Algebra 510 (2018), 331-392

 Resolutions of tempered representations of reductive p-adic groups
    joint with Eric Opdam
    Journal of Functional Analysis 265 (2013), 108-134

 Characters and growth of admissible representations of reductive p-adic groups
    joint with Ralf Meyer
    Journal de l'Institute de Mathématiques de Jussieu 11.2 (2012), 289-331

 Resolutions for representations of reductive p-adic groups via their buildings
    joint with Ralf Meyer
    Journal für die reine und angewandte Mathematik 647 (2010), 115-150


Other representation theory of p-adic groups

 Geometric structure in smooth dual and local Langlands conjecture
    joint with Anne-Marie Aubert, Paul Baum and Roger Plymen
    Japanese Journal of Mathematics 9 (2014), 99-136

  The second adjointness theorem for reductive p-adic groups
    joint with Ralf Meyer
    preprint, arXiv:1004.4290, April 2010


Hecke algebras of p-adic groups

 Hochschild homology of reductive p-adic groups
    arXiv:2203.06435, March 2022 (to appear in Journal of Noncommutative Geometry)

 Parameters of Hecke algebras for Bernstein components of p-adic groups
    preprint, arXiv:2103.13113, March 2021

 Endomorphism algebras and Hecke algebras for reductive p-adic groups
    Journal of Algebra 606 (2022), 371-470

 On completions of Hecke algebras
    pp. 207-262 in: Representations of p-adic groups
    A.-M. Aubert, M. Mishra, A. Roche, S. Spallone (eds.),
    Progress in Mathematics 328, Birkhäuser, 2019

 Periodic cyclic homology of reductive p-adic groups
    Journal of Noncommutative Geometry 3.4 (2009), 501-558


Geometric graded Hecke algebras

 On submodules of standard modules
    preprint, arXiv:2309.10401, September 2023

 Graded Hecke algebras and equivariant constructible sheaves on the nilpotent cone
    preprint, arXiv:2205.07490, May 2022

 Graded Hecke algebras, constructible sheaves and the p-adic Kazhdan--Lusztig conjecture
    preprint, arXiv:2106.03196v2, May 2022

 Graded Hecke algebras for disconnected reductive groups
    joint with Anne-Marie Aubert and Ahmed Moussaoui
    pp. 23-84 in: Geometric aspects of the trace formula, W. Müller, S. W. Shin, N. Templier (eds.)
    Simons Symposia, Springer, 2018
    arXiv:1607.02713 -- with an appendix from 2018

 Parabolically induced representations of graded Hecke algebras
    Algebras and Representation Theory 15.2 (2012), 233-271


Affine Hecke algebras

 Hermitian duals and generic representations for affine Hecke algebras
    joint with Eric Opdam
    preprint, arXiv:2309.04829, September 2023

 Affine Hecke algebras and their representations
   Indagationes Mathematicae 32.5 (2021), 1005-1082

 Extensions of tempered representations
    joint with Eric Opdam
    Geometric And Functional Analysis 23 (2013), 664-714

 On the classification of irreducible representations of affine Hecke algebras with unequal parameters
    Representation Theory 16 (2012), 1-87

 Discrete series characters for affine Hecke algebras and their formal degrees
    joint with Eric Opdam
    Acta Mathematica 205 (2010), 105-187


Homology of Hecke algebras

 Hochschild homology of twisted crossed products and twisted graded Hecke algebras
    Annals of K-theory 8.1 (2023), 81--126

 Topological K-theory of affine Hecke algebras
    Annals of K-theory 3.3 (2018), 395-460

 Hochschild homology of affine Hecke algebras
    Journal of Algebra 384 (2013), 1-35

 Homology of graded Hecke algebras
    Journal of Algebra 323 (2010), 1622-1648
    arXiv:1108.5286 -- with some corrections from 2022

 Homological algebra for affine Hecke algebras
    joint with Eric Opdam
    Advances in Mathematics 220 (2009), 1549-1601

 Periodic cyclic homology of Hecke algebras and their Schwartz completions
   preprint, arXiv:math.KT/0605042, April 2006


Noncommutative geometry

 A comparison of Hochschild homology in algebraic and smooth settings
    joint with David Kazhdan
    preprint, March 2024, arXiv:2202.06573

 Morita equivalence for k-algebras
    joint with Anne-Marie Aubert, Paul Baum and Roger Plymen
    Banach Centre Publications 120 (2020), 245-265

 Conjugacy of Levi subgroups of reductive groups and a generalization to linear algebraic groups
   J. Pure Applied Algebra, 224.6 (2020), doi.org/10.1016/j.jpaa.2019.106254

 On the Baum--Connes conjecture with coefficients for linear algebraic groups
    preprint, arXiv:1901.08807, February 2019

 Some Fréchet algebras for which the Chern character is an isomorphism
    K-Theory 36 (2005), 275-290 
    arXiv:math.KT/0505282 -- with an appendix from 2008


Theses
In September 2002 I finished my studies at the UvA with the master's thesis Lie algebra cohomology and Macdonald's conjectures

On 6 March 2007 I successfully defended my Ph.D. thesis Periodic cyclic homology of affine Hecke algebras at the Universiteit van Amsterdam. You can find the Dutch summary here.

In November 2008 the Dutch Genootschap ter bevordering van natuur-, genees- en heelkunde awarded me the Andreas Bonn medal for my research as a PhD-student.

In June 2011 I obtained my Habilitation at the Universität Göttingen. For this occasion I gave a Lehrvortrag and I wrote an extensive Forschungsbericht (in German).
cover of PhD thesis