University of Birmingham > Talks@bham > Birmingham and Warwick Algebra Seminar  > The regular representations of GL_N over finite local principal ideal rings

The regular representations of GL_N over finite local principal ideal rings

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Let F be a non-Archimedean local field with ring of integers O and maximal ideal p. T. Shintani and G. Hill independently introduced a large class of smooth representations of GLN(O), called regular representations. Roughly speaking they correspond to elements in the Lie algebra MN(O) which are regular mod p (i.e, having centraliser of dimension N). The study of regular representations of GLN(O) goes back to Shintani in the 1960s, and independently and later, Hill, who both constructed the regular representations with even conductor, but left the much harder case of odd conductor open. In recent simultaneous and independent work, Krakovski, Onn and Singla gave a construction of the regular representations of GLN(O) when the residue characteristic of O is not 2. In this talk I will present a complete construction of all the regular representations of GLN(O).

The approach is analogous to, and motivated by, the construction of supercuspidal representations of GLN(F) due to Bushnell and Kutzko. This is joint work with Shaun Stevens.

This talk is part of the Birmingham and Warwick Algebra Seminar series.

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