Outputs (20)

Rationality of twist representation zeta functions of compact p-adic analytic groups (2024)
Journal Article
Stasinski, A., & Zordan, M. (2024). Rationality of twist representation zeta functions of compact p-adic analytic groups. Transactions of the American Mathematical Society, 377, 7601-7631

We prove that for any twist rigid compact p-adic analytic group G, its twist representation zeta function is a finite sum of terms n −s i f i (p −s), where n i are natural numbers and f i (t) ∈ Q(t) are rational functions. Mero-morphic continuation a... Read More about Rationality of twist representation zeta functions of compact p-adic analytic groups.

Rationality of representation zeta functions of compact p-adic analytic groups (2023)
Journal Article
Stasinski, A., & Zordan, M. (in press). Rationality of representation zeta functions of compact p-adic analytic groups. American Journal of Mathematics,

We prove that for any FAb compact p-adic analytic group G, its representation zeta function is a finite sum of terms n −s i fi(p −s), where ni are natural numbers and fi(t) ∈ Q(t) are rational functions. Meromorphic continuation and rationality of th... Read More about Rationality of representation zeta functions of compact p-adic analytic groups.

Representatives of similarity classes of matrices over PIDs corresponding to ideal classes (2023)
Journal Article
Knight, L., & Stasinski, A. (2023). Representatives of similarity classes of matrices over PIDs corresponding to ideal classes. Glasgow Mathematical Journal, 66(1), 88-103. https://doi.org/10.1017/s0017089523000356

For a principal ideal domain A, the Latimer–MacDuffee correspondence sets up a bijection between the similarity classes of matrices in Mn(A) with irreducible characteristic polynomial f(x) and the ideal classes of the order A[x]/(f(x)). We prove that... Read More about Representatives of similarity classes of matrices over PIDs corresponding to ideal classes.

A uniform proof of the finiteness of the class group of a global field (2021)
Journal Article
Stasinski, A. (2021). A uniform proof of the finiteness of the class group of a global field. The American Mathematical Monthly, 128(3), 239-249. https://doi.org/10.1080/00029890.2021.1855036

We give a definition of a class of Dedekind domains which includes the rings of integers of global fields and give a proof that all rings in this class have finite ideal class group. We also prove that this class coincides with the class of rings of... Read More about A uniform proof of the finiteness of the class group of a global field.

Representations of SL over finite local rings of length two (2020)
Journal Article
Stasinski, A. (2021). Representations of SL over finite local rings of length two. Journal of Algebra, 566, 119-135. https://doi.org/10.1016/j.jalgebra.2020.08.036

Let Fqbe a finite field of characteristic pand let W2(Fq)be the ring of Witt vectors of length two over Fq. We prove that for any integer nsuch that pdivides n, the groups SLn(Fq[t]/t2)and SLn(W2(Fq)) have the same number of irreducible representatio... Read More about Representations of SL over finite local rings of length two.

Representation growth of compact linear groups (2019)
Journal Article
Häsä, J., & Stasinski, A. (2019). Representation growth of compact linear groups. Transactions of the American Mathematical Society, 372(2), 925-980. https://doi.org/10.1090/tran/7618

We study the representation growth of simple compact Lie groups and of SLn(O), where O is a compact discrete valuation ring, as well as the twist representation growth of GLn(O). This amounts to a study of the abscissae of convergence of the correspo... Read More about Representation growth of compact linear groups.

Representations of reductive groups over finite local rings of length two (2018)
Journal Article
Stasinski, A., & Vera-Gajardo, A. (2019). Representations of reductive groups over finite local rings of length two. Journal of Algebra, 525, 171-190. https://doi.org/10.1016/j.jalgebra.2018.11.039

LetFqbe a finite field of characteristicp, and letW2(Fq)be thering of Witt vectors of length two overFq. We prove that for any reduc-tive group schemeGoverZsuch thatpis very good forG×Fq, the groupsG(Fq[t]/t2)andG(W2(Fq))have the same number of irred... Read More about Representations of reductive groups over finite local rings of length two.

Commutators of trace zero matrices over principal ideal rings (2018)
Journal Article
Stasinski, A. (2018). Commutators of trace zero matrices over principal ideal rings. Israel Journal of Mathematics, 228(1), 211-227. https://doi.org/10.1007/s11856-018-1762-5

We prove that for every trace zero square matrix A of size at least 3 over a principal ideal ring R, there exist trace zero matrices X, Y over R such that XY−YX = A. Moreover, we show that X can be taken to be regular mod every maximal ideal of R. Th... Read More about Commutators of trace zero matrices over principal ideal rings.

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.