Zobrazeno 1 - 9
of 9
pro vyhledávání: '"Peter Patzt"'
Publikováno v:
Geometry & Topology. 25:999-1058
Let Γn(p) be the level-p principal congruence subgroup of SLn(ℤ). Borel and Serre proved that the cohomology of Γn(p) vanishes above degree n2. We study the cohomology in this top degree n2. Let 𝒯n(ℚ) denote the Tits building of SLn(ℚ). Le
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::6b256520d2a925ebb98e22afa7e717e6
https://doi.org/10.2140/gt.2021.25.999
https://doi.org/10.2140/gt.2021.25.999
Publikováno v:
Journal of Topology. 13:441-459
We prove that the Steinberg module of the special linear group of a quadratic imaginary number ring which is not Euclidean is not generated by integral apartments. Assuming the generalized Riemann hypothesis, this shows that the Steinberg module of a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::68580770981b01258a81ae59845ce511
https://doi.org/10.1112/topo.12132
https://doi.org/10.1112/topo.12132
Publikováno v:
Selecta Mathematica
Boyd, R, Hepworth, R & Patzt, P 2021, ' The homology of the Brauer algebras ', Selecta Mathematica, vol. 27, 85, pp. 1-31 . https://doi.org/10.1007/s00029-021-00697-4
Boyd, R, Hepworth, R & Patzt, P 2021, ' The homology of the Brauer algebras ', Selecta Mathematica, vol. 27, 85, pp. 1-31 . https://doi.org/10.1007/s00029-021-00697-4
This paper investigates the homology of the Brauer algebras, interpreted as appropriate Tor-groups, and shows that it is closely related to the homology of the symmetric group. Our main results show that when the defining parameter of the Brauer alge
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e111370b7a8bf27f82b0023ee4bb1a10
https://hdl.handle.net/21.11116/0000-0009-254C-921.11116/0000-0009-254E-7
https://hdl.handle.net/21.11116/0000-0009-254C-921.11116/0000-0009-254E-7
Autor:
Peter Patzt
Publikováno v:
Peter Patzt
We introduce stability categories for diagram algebras---analogues to Randal-Williams and Wahl's homogeneous categories. We use these to study representation stability properties of the Temperley--Lieb algebras, the Brauer algebras, and the partition
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ccb361b5b403c03bad424e8e02bc2b7a
http://arxiv.org/abs/2009.06346
http://arxiv.org/abs/2009.06346
Publikováno v:
Kupers, A, Miller, J, Patzt, P & Wilson, J C H 2022, ' On the generalized Bykovskii presentation of Steinberg modules ', International Mathematics Research Notices, vol. 2022, no. 13, pp. 10347–10401 . https://doi.org/10.1093/imrn/rnab028
We study presentations of the virtual dualizing modules of special linear groups of number rings, the Steinberg modules. Bykovskii gave a presentation for the Steinberg modules of the integers, and our main result is a generalization of this presenta
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::19dd9fcc63a57f241b7b44586c0a7c28
We prove a representation stability result for the codimension-one cohomology of the level three congruence subgroup of $\mathbf{SL}_n(\mathbb{Z})$. This is a special case of a question of Church-Farb-Putman which we make more precise. Our methods in
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::27ea137dfdd03c4e461657a9936667b2
http://arxiv.org/abs/1806.11131
http://arxiv.org/abs/1806.11131
Autor:
Peter Patzt
We show, finitely generated rational VIC(Q)-modules and SI(Q)-modules are uniformly representation stable and all their submodules are finitely generated. We use this to prove two conjectures of Church and Farb, which state that the quotients of the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::76b000f8e1a047664ada8101e11b2e23
https://refubium.fu-berlin.de/handle/fub188/2490
https://refubium.fu-berlin.de/handle/fub188/2490
Autor:
Xiaolei Wu, Peter Patzt
Publikováno v:
Algebraic & Geometric Topology
Algebr. Geom. Topol. 16, no. 4 (2016), 2365-2377
Algebr. Geom. Topol. 16, no. 4 (2016), 2365-2377
We prove homological stability for a twisted version of the Houghton groups and their multidimensional analogues. Based on this, we can describe the homology of the Houghton groups and that of their multidimensional analogues over constant noetherian
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e0d6e1f5db58cb032f77ef26f162c503
https://hdl.handle.net/21.11116/0000-0004-0E2B-E21.11116/0000-0004-0E2C-D21.11116/0000-0004-0E29-0
https://hdl.handle.net/21.11116/0000-0004-0E2B-E21.11116/0000-0004-0E2C-D21.11116/0000-0004-0E29-0
Autor:
Peter Patzt
Publikováno v:
Peter Patzt
We give a new categorical way to construct the central stability homology of Putman and Sam and explain how it can be used in the context of representation stability and homological stability. In contrast to them, we cover categories with infinite au
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7a26d2a005d76b2ef619de839e00b748
https://arxiv.org/abs/1704.04128
https://arxiv.org/abs/1704.04128