A Random Walk on the Indecomposable Summands of Tensor Products of Modular Representations of SL2 (Fp). / McDowell, Eoghan.

In: Algebras and Representation Theory, 12.03.2021.

Research output: Contribution to journalArticlepeer-review

E-pub ahead of print

Standard

A Random Walk on the Indecomposable Summands of Tensor Products of Modular Representations of SL2 (Fp). / McDowell, Eoghan.

In: Algebras and Representation Theory, 12.03.2021.

Research output: Contribution to journalArticlepeer-review

Harvard

APA

Vancouver

Author

BibTeX

@article{ec8e2f4af447496e8cb2e31782f16eb9,
title = "A Random Walk on the Indecomposable Summands of Tensor Products of Modular Representations of SL2 (Fp)",
abstract = "In this paper we introduce a novel family of Markov chains on the simple representations of SL_2(F_p) in defining characteristic, defined by tensoring with a fixed simple module and choosing an indecomposable non-projective summand. We show these chains are reversible and find their connected components and their stationary distributions. We draw connections between the properties of the chain and the representation theory of SL_2(F_p), emphasising symmetries of the tensor product. We also provide an elementary proof of the decomposition of tensor products of simple SL_2(F_p)-representations.",
author = "Eoghan McDowell",
year = "2021",
month = mar,
day = "12",
doi = "10.1007/s10468-021-10034-0",
language = "English",
journal = "Algebras and Representation Theory",
issn = "1386-923X",
publisher = "Springer Netherlands",

}

RIS

TY - JOUR

T1 - A Random Walk on the Indecomposable Summands of Tensor Products of Modular Representations of SL2 (Fp)

AU - McDowell, Eoghan

PY - 2021/3/12

Y1 - 2021/3/12

N2 - In this paper we introduce a novel family of Markov chains on the simple representations of SL_2(F_p) in defining characteristic, defined by tensoring with a fixed simple module and choosing an indecomposable non-projective summand. We show these chains are reversible and find their connected components and their stationary distributions. We draw connections between the properties of the chain and the representation theory of SL_2(F_p), emphasising symmetries of the tensor product. We also provide an elementary proof of the decomposition of tensor products of simple SL_2(F_p)-representations.

AB - In this paper we introduce a novel family of Markov chains on the simple representations of SL_2(F_p) in defining characteristic, defined by tensoring with a fixed simple module and choosing an indecomposable non-projective summand. We show these chains are reversible and find their connected components and their stationary distributions. We draw connections between the properties of the chain and the representation theory of SL_2(F_p), emphasising symmetries of the tensor product. We also provide an elementary proof of the decomposition of tensor products of simple SL_2(F_p)-representations.

U2 - 10.1007/s10468-021-10034-0

DO - 10.1007/s10468-021-10034-0

M3 - Article

JO - Algebras and Representation Theory

JF - Algebras and Representation Theory

SN - 1386-923X

ER -