Locally algebraic vectors in the Breuil – Herzig ordinary part

Locally Algebraic Vectors in the Breuil-herzig Ordinary Part

For a fairly general reductive group G/Qp , we explicitly compute the space of locally algebraic vectors in the Breuil-Herzig construction Π(ρ)ord, for a potentially semistable Borel-valued representation ρ of Gal(Q̄p/Qp). The point being we deal with the whole representation, not just its socle – and we go beyond GLn(Qp). In the case of GL2(Qp), this relation is one of the key properties of the...

Ordinary representations of G(Qp) and fundamental algebraic representations

Locally analytic vectors of unitary principal series of GL2(Qp) I

For V a 2-dimensional p-adic representation of GQp , we denote by B(V ) the admissible unitary representation of GL2(Qp) attached to V under the p-adic local Langlands correspondence of GL2(Qp) initiated by Breuil. In this article, building on the works of Berger-Breuil and Colmez, we determine the locally analytic vectors B(V )an of B(V ) when V is irreducible, crystabelian and Frobenius semi-...

Realization of locally extended affine Lie algebras of type $A_1$

Locally extended affine Lie algebras were introduced by Morita and Yoshii in [J. Algebra 301(1) (2006), 59-81] as a natural generalization of extended affine Lie algebras. After that, various generalizations of these Lie algebras have been investigated by others. It is known that a locally extended affine Lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...

The study of relation between existence of admissible vectors and amenability and compactness of a locally compact group

The existence of admissible vectors for a locally compact group is closely related to the group's profile. In the compact groups, according to Peter-weyl theorem, every irreducible representation has admissible vector. In this paper, the conditions under which the inverse of this case is being investigated has been investigated. Conditions such as views that are admissible and stable will get c...