noindent We have two goals in this paper. First, we investigate and construct cofree coalgebras over $n$-representations of quivers, limits and colimits of $n$-representations of quivers, and limits and colimits of coalgebras in the monoidal categories of $n$-representations of quivers. Second, for any given quivers $mathit{Q}_1$,$mathit{Q}_2$,..., $mathit{Q}_n$, we construct a new quiver $math...

Let π be a simple supercuspidal representation of the split even special orthogonal group. We compute Rankin-Selberg γ-factors for rank 1-twists by quadratic tamely ramified characters F*. Our results determine certain 1-dimensional summands Langlands parameter. Assuming an expected analogue work Blondel, Henniart, and Stevens, these completely parameter π.

In this paper we provide a geometric framework for the study of characters of depth-zero representations of unramified groups over local fields with finite residue fields which is built directly on Lusztig's theory of character sheaves for groups over finite fields and uses ideas due to Schneider-Stuhler. Specifically, we introduce a class of coefficient systems on Bruhat-Tits buildings of perv...

Let OK = FqJπK be the ring of power series in one variable over a finite field, and let K be its fraction field. We introduce the notion of a “formal K-vector space”; this is a certain kind of K-vector space object in the category of formal schemes. This concept runs parallel to the established notion of a formal OK-module, but in many ways formal K-vector spaces are much simpler objects. Our m...

‎We consider Albeverio's linear representations of the braid groups $B_3$ and $B_4$‎. ‎We specialize the indeterminates used in defining these representations to non zero complex numbers‎. ‎We then consider the tensor products of the representations of $B_3$ and the tensor products of those of $B_4$‎. ‎We then determine necessary and sufficient conditions that guarantee the irreducibility of th...

We complete the Wilf classification of signed patterns of length 5 for both signed permutations and signed involutions. New general equivalences of patterns are given which prove Jaggard’s conjectures concerning involutions in the symmetric group avoiding certain patterns of length 5 and 6. In this way, we also complete the Wilf classification of S5, S6, and S7 for both permutations and involut...

Let G be a unitary, symplectic or orthogonal group over a non-archimedean local field of residual characteristic different from 2, considered as the fixed point subgroup in a general linear group G̃ of an involution. Following [7] and [13], we generalize the notion of a semisimple character for G̃ and for G. In particular, following the formalism of [4], we show that these semisimple characters h...

The charge-asymmetry observed in a recent CPLEAR experiment was interpreted by the authors as a direct observation of T-noninvariance. While this is the simplest and most natural inference, and the observed effect agrees in sign and magnitude with theoretical expectation, adherents of T-invariance may argue that other interpretations are also possible. If K and K̄ are produced equally in p̄p anni...

How do political institutions shape government size and redistributional policies? An empirical model proposes a possible framework to evaluate sign and magnitude of the relation. Political institutions are classified in complementary constraints, namely political competition, competition in executive recruitment and constraints on the executive. Results show that the stronger democratic instit...