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INTRODUCTION Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics and quantum field theory. In this letter Dedekind made the following observation: take the(More)
Following the works by Wiegmann–Zabrodin, Elbau–Felder, Hedenmalm–Maka-rov, and others, we consider the normal matrix model with an arbitrary potential function, and explain how the problem of finding the support domain for the asymptotic eigenvalue density of such matrices (when the size of the matrices goes to infinity) is related to the problem of(More)
We start the general structure theory of not necessarily semisimple finite tensor categories, generalizing the results in the semi-simple case (i. e. for fusion categories), obtained recently in our joint work with D. Nikshych. In particular, we generalize to the categorical setting the Hopf and quasi-Hopf algebra freeness theorems due to Nichols–Zoeller(More)
Let W be a finite Coxeter group in a Euclidean vector space V , and let m be a W-invariant Z+-valued function on the set of reflections in W. Chalykh and Veselov introduced an interesting algebra Qm, called the algebra of m-quasi-invariants for W , such that C[V ] W ⊆ Qm ⊆ C[V ], Q0 = C[V ], and Qm ⊇ Q m whenever m ≤ m. Namely, Qm is the algebra of quantum(More)