Cornelius Pillen

Publications

• Restricting Rational Modules to Frobenius Kernels , coauthored with C.P. Bendel, D.K. Nakano, P. Sobaje, J., preprint.                                                      
• On Donkin's Tilting Module Conjecture III: New Generic Lower Bound, coauthored with C.P. Bendel, D.K. Nakano, P. Sobaje, J. Algebra, DOI: 10.1016/j.jalgebra.2023.07.001, (2023).  
                                                    

• On Donkin's Tilting Module Conjecture II: Counterexamples, coauthored with C.P. Bendel, D.K. Nakano, P. Sobaje, Compositio Math. 160, 1167 --1193, (2024).

• On Donkin's Tilting Module Conjecture I: Lowering the Prime, coauthored with C.P. Bendel, D.K. Nakano, P. Sobaje, Represent. Theory 26, 455 - 497, (2022).

• The Spider and the Fly, Alabama Journal of Mathematics, Vol. 25, (2022).                                                                                                     

• Counterexamples to the Tilting and (p,r)-Filtration Conjectures, coauthored with C.P. Bendel, D.K. Nakano, P. Sobaje, Journal fuer die Reine und Angewandte Mathematik (Crelle's Journal) 767, 193 -202, (2020).

• On Tensoring with the Steinberg Representation, coauthored with C.P. Bendel, D.K. Nakano, P. Sobaje, Transformation Groups 25, no. 4, 981 - 1008, (2020).

• Third Cohomology of Frobenius Kernels and Related Structures, coauthored with C.P. Bendel, D.K. Nakano, Lie algebras, Lie superalgebras, vertex algebras and related topics, 81 - 118, Proc. Sympos. Pure Math., 92, Amer. Math. Soc., Providence, RI, (2016).

• Bounding Extensions for Finite Groups and Frobenius Kernels, coauthored with C.P. Bendel, D.K. Nakano, B.J. Parshall, L.L. Scott and D.I. Stewart, Algebras and Representation Theory 18, no. 3, 739 -760, (2015).

• Extensions for Finite Chavalley Groups III: Rational and Generic Cohomology, coauthored with C.P. Bendel, D.K. Nakano, Adv. Math. , 262, 484-519, (2014).

• Bounding the Dimensions of Rational Cohomology Groups, coauthored with C.P. Bendel, B.D. Boe, C.M. Drupieski, D.K. Nakano, B.J. Parshall, and C.B. Wright, Current Developments and Retrospectives in Lie Theory, Algebraic Methods, Developments in Mathematics 38, Springer Verlag, (2014).

• Cohomology for Quantum Groups via the Geometry of the Nullcone, coauthored with C.P. Bendel, D.K. Nakano and B.J. Parshall, Memoirs of the AMS , 229, no 1077, (2014).

• On the Vanishing Ranges for the Cohomology of Finite Groups of Lie Type II, coauthored with C.P. Bendel and D.K. Nakano, Recent Developments in Lie Algebras, Groups, and Representation Theory, Proceedings of Symposia in Pure Mathematics, Volume 86, (2012).

• On the Vanishing Ranges for the Cohomology of Finite Groups of Lie Type, coauthored with C.P. Bendel, D.K. Nakano, International Mathematics Research Notices, rnr130, doi:10.1093/imrn/rnr130, (2011).

• Second Cohomology Groups for Frobenius kernels and related structures, coauthored with C. Bendel and D.K. Nakano, Adv. Math. , 201, 162-197, (2007).

• Extensions for finite groups of Lie type II: Filtering the truncated induction functor, coauthored with C. Bendel and D.K. Nakano, Representations of Algebraic Groups, Quantum Groups, and Lie Algebras, Contemporary Mathematics, Vol. 413, AMS (2006).

• Self-Extensions for the finite symplectic groups via algebraic groups, Representations of Algebraic Groups, Quantum Groups, and Lie Algebras, Contemporary Mathematics, Vol. 413, AMS (2006).

• Extensions for finite groups of Lie type: twisted case , coauthored with C. Bendel and D.K. Nakano, Finite Groups 2003, de Gruyter, New York, 29-46 (2004).

• Extensions for Frobenius Kernels, coauthored with C. Bendel and D.K. Nakano, J. Algebra , 272, 476-511, (2004).

• Extensions for finite Chevalley groups II, coauthored with C. Bendel and D.K. Nakano, Trans. Amer. Math. Soc., 354, 4421-4454, (2002).

• Extensions for finite Chevalley groups I, coauthored with C. Bendel and D.K. Nakano, Adv. Math. , 183, 380-408, (2004).

• On comparing the cohomology of algebraic groups, finite Chevalley groups and Frobenius kernels , coauthored with C. Bendel and D.K. Nakano, Journal of Pure and Applied Algebra, 163, 119-146, (2001).

• Generic Patterns for Extensions of Simple Modules for Finite Chevalley Groups, J. Algebra, 212, 419-427, (1999).

• Loewy Series for Principal Series Representations of Finite Chevalley Groups, J. Algebra, 189, 101-124, (1997).

• The First Cartan Invariant of a Finite Group of Lie Type for Large p, J. Algebra, 174, 934-947 (1995).

• Reduction Modulo p of some Deligne-Lusztig Characters, Arch. Math., Vol. 61, 421-433 (1993).

• Tensor Products of Modules with Restricted Highest Weights, Comm. Algebra, 21(10), 3647-3661 (1993).

• Tensor Products and Injectives for Groups of Lie Type, Ph.D. Thesis, University of Massachusetts, 1992.

• The Sum of an Abelian and a Nilpotent Lie Algebra is Solvable, [German], Results in Mathematics, Vol. 2 (1987), 117-121, MR 88e:17006.

• Criteria for Solvability of Lie Algebras with Abelian and Nilpotent Summands, [German], Diplomarbeit, Albert-Ludwigs-Universität, Freiburg, 1986.

Teaching

For information on my classes please go to USAonline (Canvas).