Algebra & Number Theory
- Algebra Number Theory
- Volume 14, Number 1 (2020), 119-154.
Stability in the homology of unipotent groups
Let be a (not necessarily commutative) ring whose additive group is finitely generated and let be the group of upper-triangular unipotent matrices over . We study how the homology groups of vary with from the point of view of representation stability. Our main theorem asserts that if for each we have representations of over a ring that are appropriately compatible and satisfy suitable finiteness hypotheses, then the rule defines a finitely generated -module. As a consequence, if is a field then is eventually equal to a polynomial in . We also prove similar results for the Iwahori subgroups of for number rings .
Algebra Number Theory, Volume 14, Number 1 (2020), 119-154.
Received: 19 December 2018
Accepted: 18 August 2019
First available in Project Euclid: 7 April 2020
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Putman, Andrew; Sam, Steven V; Snowden, Andrew. Stability in the homology of unipotent groups. Algebra Number Theory 14 (2020), no. 1, 119--154. doi:10.2140/ant.2020.14.119. https://projecteuclid.org/euclid.ant/1586224821