TY - JOUR
T1 - Spanning Configurations and Representation Stability
AU - Pawlowski, Brendan
AU - Ramos, Eric
AU - Rhoades, Brendon
N1 - Publisher Copyright:
© The authors.
PY - 2023
Y1 - 2023
N2 - Let V1, V2, V3, … be a sequence of Q-vector spaces where Vn carries an action of Sn. Representation stability and multiplicity stability are two related notions of when the sequence Vn has a limit. An important source of stability phenomena arises when Vn is the dth homology group (for fixed d) of the configuration space of n distinct points in some fixed topological space X. We replace these configuration spaces with moduli spaces of tuples (W1, …, Wn) of subspaces of a fixed complex vector space CN such that W1 + · · · + Wn = CN. These include the varieties of spanning line configurations which are tied to the Delta Conjecture of symmetric function theory.
AB - Let V1, V2, V3, … be a sequence of Q-vector spaces where Vn carries an action of Sn. Representation stability and multiplicity stability are two related notions of when the sequence Vn has a limit. An important source of stability phenomena arises when Vn is the dth homology group (for fixed d) of the configuration space of n distinct points in some fixed topological space X. We replace these configuration spaces with moduli spaces of tuples (W1, …, Wn) of subspaces of a fixed complex vector space CN such that W1 + · · · + Wn = CN. These include the varieties of spanning line configurations which are tied to the Delta Conjecture of symmetric function theory.
UR - http://www.scopus.com/inward/record.url?scp=85146171223&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85146171223&partnerID=8YFLogxK
U2 - 10.37236/11136
DO - 10.37236/11136
M3 - Article
AN - SCOPUS:85146171223
VL - 30
JO - Electronic Journal of Combinatorics
JF - Electronic Journal of Combinatorics
IS - 1
M1 - P1.7
ER -