Monoid deformations and group representations
نویسندگان
چکیده
منابع مشابه
Group Invariance and Stability to Deformations of Deep Convolutional Representations
In this paper, we study deep signal representations that are invariant to groups of transformations and stable to the action of diffeomorphisms without losing signal information. This is achieved by generalizing the multilayer kernel construction introduced in the context of convolutional kernel networks and by studying the geometry of the corresponding reproducing kernel Hilbert space. We show...
متن کاملRepresentations of the Renner Monoid
We describe irreducible representations and character formulas of the Renner monoids for reductive monoids, which generalizes the Munn-Solomon representation theory of rook monoids to any Renner monoids. The type map and polytope associated with reductive monoids play a crucial role in our work. It turns out that the irreducible representations of certain parabolic subgroups of the Weyl groups ...
متن کاملRepresentations of the rook monoid
Let n be a positive integer and let n = {1, . . . , n}. Let R be the set of all oneto-one maps σ with domain I (σ ) ⊆ n and range J (σ) ⊆ n. If i ∈ I (σ ) let iσ denote the image of i under σ . There is an associative product (σ, τ ) → στ on R defined by composition of maps: i(στ)= (iσ )τ if i ∈ I (σ ) and iσ ∈ I (τ ). Thus the domain I (στ) consists of all i ∈ I (σ ) such that iσ ∈ I (τ ). The...
متن کاملThe Bihecke Monoid of a Finite Coxeter Group and Its Representations
For any finite Coxeter group W , we introduce two new objects: its cutting poset and its biHecke monoid. The cutting poset, constructed using a generalization of the notion of blocks in permutation matrices, almost forms a lattice on W . The construction of the biHecke monoid relies on the usual combinatorial model for the 0-Hecke algebra H0(W ), that is, for the symmetric group, the algebra (o...
متن کاملThe monoid of families of quiver representations
The aim of this paper is to develop an algebraic tool, namely the monoid structure on families of quiver representations as stated in the title, which is directly related both to quantized Kac-Moody algebras, and to geometric properties of varieties of representations. Although this new structure is far from being understood in detail, it it easily accessible to explicit calculations, and it pr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1998
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(97)00125-4