Outputs (3)

The regular representations of GLN over finite local principal ideal rings (2017)
Journal Article
Stasinski, A., & Stevens, S. (2017). The regular representations of GLN over finite local principal ideal rings. Bulletin of the London Mathematical Society, 49(6), 1066-1084. https://doi.org/10.1112/blms.12099

Let o o be the ring of integers in a non-Archimedean local field with finite residue field, p p its maximal ideal, and r ⩾ 2 r⩾2 an integer. An irreducible representation of the finite group G r = GL N ( o / p r ) Gr=GLN(o/pr), for an integer N ⩾ 2 N... Read More about The regular representations of GLN over finite local principal ideal rings.

The algebraisation of higher Deligne–Lusztig representations (2017)
Journal Article
Chen, Z., & Stasinski, A. (2017). The algebraisation of higher Deligne–Lusztig representations. Selecta Mathematica (New Series), 23(4), 2907-2926. https://doi.org/10.1007/s00029-017-0349-z

In this paper we study higher Deligne–Lusztig representations of reductive groups over finite quotients of discrete valuation rings. At even levels, we show that these geometrically constructed representations, defined by Lusztig, coincide with certa... Read More about The algebraisation of higher Deligne–Lusztig representations.

Representations of GL_N over finite local principal ideal rings: an overview (2017)
Conference Proceeding
Stasinski, A. (2017). Representations of GL_N over finite local principal ideal rings: an overview. In F. Brumley, M. P. Gómez Aparicio, & A. Mínguez (Eds.), Around Langlands correspondences : international conference on around Langlands correspondences, June 17-20, 2015, Universite Paris Sud, Orsay, France ; proceedings (337-358). https://doi.org/10.1090/conm/691/13902

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.