Related papers: Equivariant differential characters and symplectic…
We use explicit pseudoholomorphic curve techniques (without virtual perturbations) to define a sequence of symplectic capacities analogous to those defined recently by the second named author using symplectic field theory. We then compute…
We present three equivalent definitions of $S^1$-equivariant symplectic homology. We show that, using rational coefficients, the positive part of $S^1$-equivariant symplectic homology is isomorphic to linearized contact homology, when the…
We begin the study of character sheaves on a not necessarily connected reductive group, extending the known theory for connected groups.
We perform separation of variables for the symplectic Weyl character using Sklyanin's scheme. Viewing the characters as eigenfunctions of a quantum integrable system, we explicitly construct the separating operator using the Q-operator…
This paper introduces equivariant hamiltonian flows, a method for learning expressive densities that are invariant with respect to a known Lie-algebra of local symmetry transformations while providing an equivariant representation of the…
In this work, generalized principal bundles modelled by Lie group bundle actions are investigated. In particular, the definition of equivariant connections in these bundles, associated to Lie group bundle connections, is provided, together…
We restrict irreducible characters of alternating groups of degree divisible by $p$ to their Sylow $p$-subgroups and study the number of linear constituents.
In a polydiagonal subspace of the Euclidean space, certain components of the vectors are equal (synchrony) or opposite (anti-synchrony). Polydiagonal subspaces invariant under a matrix have many applications in graph theory and dynamical…
We construct supercharacter theories of finite unipotent groups in the orthogonal, symplectic and unitary types. Our method utilizes group actions in a manner analogous to that of Diaconis and Isaacs in their construction of supercharacters…
We construct for an equivariant cohomology theory for proper equivariant CW-complexes an equivariant Chern character, provided that certain conditions about the coefficients are satisfied. These conditions are fulfilled if the coefficients…
We obtain an explicit presentation of the equivariant cobordism ring of a complete flag variety. An immediate corollary is a Borel presentation of the ordinary cobordism ring. Another application is an equivariant Schubert calculus in…
We construct versal and equimultiple versal deformations of the parametrization of a Legendrian curve.
The meaning of quantum group transformation properties is discussed in some detail by comparing the (co)actions of the quantum group with those of the corresponding Lie group, both of which have the same algebraic (matrix) form of the…
We present examples of prequantizations over integral symplectic manifolds which admit infinitely many smoothly trivial contact mapping classes. These classes are given by the connected components of the strict contactomorphism group which…
In this note, we give a geometric expression for the multiplicities of the equivariant index of a Dirac operator twisted by a line bundle.
In this contribution we use the model of discrete spaces that we have put forward in former articles to give an interpretation to the phenomena of quantum entanglement and quantum states reduction that rests upon a new way of considering…
We relate the quantum Steenrod square to Seidel's equivariant pair-of-pants product for open convex symplectic manifolds that are either monotone or exact, using an equivariant version of the PSS isomorphism. We proceed similarly for…
This paper introduces an inner product on chain complexes of finite simplicial complexes that is well-adapted to the harmonic study of subdivisions. Its definition utilizes a decomposition of the chain spaces that suggests a sequence of…
We define formal orbifolds over an algebraically closed field of arbitrary characteristic as curves together with some branch data. Their \'etale coverings and their fundamental groups are also defined. These fundamental group approximates…
We introduce the notion of (twisted) quiver representations in abelian categories and study the category of such representations. We construct standard resolutions and coresolutions of quiver representations and study basic homological…