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Representations of GL_N over finite local principal ideal rings: an overview (2017)
Presentation / Conference Contribution
Stasinski, A. (2015, June). Representations of GL_N over finite local principal ideal rings: an overview. Presented at Around Langlands Correspondences, Paris, France

We give a survey of the representation theory of GLN over finite local principal ideal rings via Clifford theory, with an emphasis on the construction of regular representations. We review results of Shintani and Hill, and the generalisation of Takas... Read More about Representations of GL_N over finite local principal ideal rings: an overview.

Representation zeta functions of some nilpotent groups associated to prehomogeneous vector spaces (2016)
Journal Article
Stasinski, A., & Voll, C. (2017). Representation zeta functions of some nilpotent groups associated to prehomogeneous vector spaces. Forum Mathematicum, 29(3), 717-734. https://doi.org/10.1515/forum-2015-0099

We compute the representation zeta functions of some finitely generated nilpotent groups associated to unipotent group schemes over rings of integers in number fields. These group schemes are defined by Lie lattices whose presentations are modelled o... Read More about Representation zeta functions of some nilpotent groups associated to prehomogeneous vector spaces.

Similarity and commutators of matrices over principal ideal rings (2015)
Journal Article
Stasinski, A. (2016). Similarity and commutators of matrices over principal ideal rings. Transactions of the American Mathematical Society, 368(4), 2333-2354. https://doi.org/10.1090/tran/6402

We prove that if is a principal ideal ring and is a matrix with trace zero, then is a commutator, that is, for some . This generalises the corresponding result over fields due to Albert and Muckenhoupt, as well as that over due to Laffey and Reams, a... Read More about Similarity and commutators of matrices over principal ideal rings.

Representation zeta functions of nilpotent groups and generating functions for Weyl groups of type B (2014)
Journal Article
Stasinski, A., & Voll, C. (2014). Representation zeta functions of nilpotent groups and generating functions for Weyl groups of type B. American Journal of Mathematics, 136(2), 501-550. https://doi.org/10.1353/ajm.2014.0010

We study representation zeta functions of finitely generated, torsion-free nilpotent groups which are groups of rational points of unipotent group schemes over rings of integers of number fields. Using the Kirillov orbit method and $\frak{p}$-adic in... Read More about Representation zeta functions of nilpotent groups and generating functions for Weyl groups of type B.

A New Statistic on the Hyperoctahedral Groups (2013)
Journal Article
Stasinski, A., & Voll, C. (2013). A New Statistic on the Hyperoctahedral Groups. Electronic Journal of Combinatorics, 20(3), Article 50

We introduce a new statistic on the hyperoctahedral groups (Coxeter groups of type B), and give a conjectural formula for its signed distributions over arbitrary descent classes. The statistic is analogous to the classical Coxeter length function, an... Read More about A New Statistic on the Hyperoctahedral Groups.

Reductive group schemes, the Greenberg functor, and associated algebraic groups (2012)
Journal Article
Stasinski, A. (2012). Reductive group schemes, the Greenberg functor, and associated algebraic groups. Journal of Pure and Applied Algebra, 216(5), 1092-1101. https://doi.org/10.1016/j.jpaa.2011.10.027

Let AA be an Artinian local ring with algebraically closed residue field kk, and let View the MathML sourceG be an affine smooth group scheme over AA. The Greenberg functor FF associates to View the MathML sourceG a linear algebraic group View the Ma... Read More about Reductive group schemes, the Greenberg functor, and associated algebraic groups.

Extended Deligne–Lusztig varieties for general and special linear groups (2011)
Journal Article
Stasinski, A. (2011). Extended Deligne–Lusztig varieties for general and special linear groups. Advances in Mathematics, 226(3), 2825-2853. https://doi.org/10.1016/j.aim.2010.10.010

We give a generalisation of Deligne–Lusztig varieties for general and special linear groups over finite quotients of the ring of integers in a non-archimedean local field. Previously, a generalisation was given by Lusztig by attaching certain varieti... Read More about Extended Deligne–Lusztig varieties for general and special linear groups.

On cuspidal Representations of General Linear Groups over Discrete Valuation Rings (2010)
Journal Article
Aubert, A., Onn, U., Prasad, A., & Stasinski, A. (2010). On cuspidal Representations of General Linear Groups over Discrete Valuation Rings. Israel Journal of Mathematics, 175(1), 391-420. https://doi.org/10.1007/s11856-010-0016-y

We define a new notion of cuspidality for representations of GL n over a finite quotient o k of the ring of integers o of a non-Archimedean local field F using geometric and infinitesimal induction functors, which involve automorphism groups G λ of t... Read More about On cuspidal Representations of General Linear Groups over Discrete Valuation Rings.

Unramified representations of reductive groups over finite rings (2009)
Journal Article
Stasinski, A. (2009). Unramified representations of reductive groups over finite rings. Representation Theory, 13, 636-656. https://doi.org/10.1090/s1088-4165-09-00350-1

Lusztig has given a construction of certain representations of reductive groups over finite local principal ideal rings of characteristic $ p$, extending the construction of Deligne and Lusztig of representations of reductive groups over finite field... Read More about Unramified representations of reductive groups over finite rings.