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Two main motivations: The first is representation stability: a generalization of homological stability in the presence of group actions which was introduced by Church and Farb. For symmetric group actions, this is formalized in the notion of FI-modules, introduced by Church, Ellenberg, and Farb. FI-modules turn out to be modules over a twisted commutative(More)
Fix a field K and let Q = (Q 0 , Q 1) be a loopless quiver. We consider finite-dimensional representations of Q over K. Each representation has a naturally associated dimension vector. Let ∆ = (a ij) be the Cartan matrix associated to the underlying graph of Q and let g = g(∆) be the associated Kac–Moody algebra. Theorem 1.1 (Kac). Assume K is algebraically(More)
Many difference sets have been found and the existence of others disproved under certain parameter sets. The Center for Communications Research at La Jolla gives a list of many open cases in which the existence of a cyclic difference set is unknown. Using multiplier theorems and techniques from algebraic number theory, we tackle this list of open parameter(More)
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