Intersecting defects in gauge theory, quantum spin chains, and Knizhnik-Zamolodchikov equations

We propose an interesting BPS/CFT correspondence playground: the correlation function of two intersecting half-BPS surface defects in four-dimensional $$ \mathcal{N} $$ N = 2 supersymmetric SU(N) gauge theory with 2N fundamental hypermultiplets. We show it satisfies a difference equation, the fractional quantum T-Q relation. Its Fourier transform is the 5-point conformal block of the $$ {\hat{\mathfrak{sl}}}_N $$ sl ̂ N current algebra with one of the vertex operators corresponding to the N-dimensional $$ {\mathfrak{sl}}_N $$ sl N representation, which we demonstrate with the help of the Knizhnik-Zamolodchikov equation. We also identify the correlator with a state of the $$ {XXX}_{{\mathfrak{sl}}_2} $$ XXX sl 2 spin chain of N Heisenberg-Weyl modules over Y ($$ {\mathfrak{sl}}_2 $$ sl 2 ). We discuss the associated quantum Lax operators, and connections to isomonodromic deformations.

Integral Ext groups between hook Weyl modules

Υπολογίζουμε τις ομάδες ακέραιων επεκτάσεων μεταξύ Βάιλ προτύπων σχήματος χουκ σε βαθμούς 1 και 2 και το μέγιστο βαθμό όπου αυτές είναι μη μηδενικές.

Weyl modules and Weyl functors for hyper-map algebras

We investigate the representations of the hyperalgebras associated to the map algebras [Formula: see text], where [Formula: see text] is any finite-dimensional complex simple Lie algebra and [Formula: see text] is any associative commutative unitary algebra with a multiplicatively closed basis. We consider the natural definition of the local and global Weyl modules, and the Weyl functor for these algebras. Under certain conditions, we prove that these modules satisfy certain universal properties, and we also give conditions for the local or global Weyl modules to be finite-dimensional or finitely generated, respectively.