Parabolic induction and restriction functors for rational Cherednik algebras by Bezrukavnikov, Roman, Etingof, Pavel I.

“…However, a naive attempt to do so fails: the definition of parabolic induction and restriction functors for finite and affine Hecke algebras uses the fact that the Hecke algebra attached to a parabolic subgroup can be embedded into the Hecke algebra attached to the whole group, which is not the case in the double affine setting.…”
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Classical W-Algebras and Generalized Drinfeld–Sokolov Hierarchies for Minimal and Short Nilpotents by Valeri, Daniele, Sole, Alberto De, Kac, Victor

“…We derive explicit formulas for λ-brackets of the affine classical W-algebras attached to the minimal and short nilpotent elements of any simple Lie algebra g. …”
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Character sheaves on disconnected groups, VII by Lusztig, G

“…As an application, we attach to any parabolic character sheaf the orbit of a tame local system on the maximal torus under a subgroup of the Weyl group.…”
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Springer Fibers for the Minimal and the Minimal Special Nilpotent Orbits by Kim, Dongkwan

“…As a result, we give an answer to the conjecture of Humphreys regarding some graphs attached to Springer fibers.…”
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Hidden diagonal integrability of q-Hahn vertex model and Beta polymer model by Korotkikh, Sergei

“…The main distinctive feature of our model is a new family of parameters attached to diagonals rather than to rows or columns, like in other similar models. …”
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Yangians versus minimal W-algebras: A surprising coincidence by Kac, Victor G, Frajria, Pierluigi Möseneder, Papi, Paolo

“…We prove that the singularities of the R-matrix R(k) of the minimal quantization of the adjoint representation of the Yangian Y of a finite dimensional simple Lie algebra are the opposite of the roots of the monic polynomial p(k) entering in the OPE expansions of quantum fields of conformal weight 3/2 of the universal minimal affine W-algebra at level k attached to .…”
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The Goodwillie tower for S[superscript 1] and Kuhn's Theorem by Behrens, Mark Joseph

“…We analyze the homological behavior of the attaching maps in the 2–local Goodwillie tower of the identity evaluated at S¹. …”
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Cherednik and Hecke Algebras of Varieties with a Finite Group Action by Etingof, Pavel I

“…In this paper, we define global analogs of Cherednik algebras, attached to any smooth algebraic or analytic variety X with a finite group G of automorphisms of X. …”
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Lagrangian caps by Eliashberg, Yakov, Murphy, Emmy

“…We prove, in particular, that in the complement of the unit ball B in the standard symplectic R[superscript 2n], 2n ≥ 6 , there exists an embedded Lagrangian n-disc transversely attached to B along its Legendrian boundary, which is loose in the sense of Murphy (Loose Legendrian embeddings in high dimensional contact manifolds, arXiv:1201.2245, 2013).…”
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On characters of irreducible highest weight modules of negative integer level over affine lie algebras by Kac, Victor, Wakimoto, Minoru

“…We prove a character formula for irreducible highest weight modules over a simple affine vertex algebra of level k, attached to a simple Lie algebra g, which are locally g-finite, in the cases when g is of type An and Cn (n≥2) and k = −1. …”
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POISSON TRACES AND D-MODULES ON POISSON VARIETIES by Etingof, Pavel I., Schedler, Travis

“…To every Poisson algebraic variety X over an algebraically closed field of characteristic zero, we canonically attach a right D-module M(X) on X. If X is affine, solutions of M(X) in the space of algebraic distributions on X are Poisson traces on X, i.e. distributions invariant under Hamiltonian flow. …”
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Finite Dimensional Hopf Actions on Central Division Algebras by Cuadra-Diaz, Juan, Etingof, Pavel I

“…Finally, we construct Hopf-Galois actions on division algebras of twisted group algebras attached to bijective cocycles.…”
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p-adic dimensions in symmetric tensor categories in characteristic p by Etingof, Pavel I, Harman, Nate, Ostrik, Victor

“…To every object X of a symmetric tensor category over a field of characteristic p > 0 we attach p-adic integers Dim+(X) and Dim−(X) whose reduction modulo p is the categorical dimension dim(X) of X, coinciding with the usual dimension when X is a vector space. …”
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The Small Quantum Group as a Quantum Double by Etingof, Pavel I., Gelaki, Shlomo

“…We prove that the quantum double of the quasi-Hopf algebra View the MathML source of We prove that the quantum double of the quasi-Hopf algebra Aq(g) of dimension ndimg attached in [P. Etingof, S. Gelaki, On radically graded finite-dimensional quasi-Hopf algebras, Mosc. …”
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Representations of rational Cherednik algebras of G(m,r,n) in positive characteristic by Devadas, Sheela, Sam, Steven V.

“…We study lowest-weight irreducible representations of rational Cherednik algebras attached to the complex reflection groups G(m,r,n) in characteristic p. …”
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Spectral Action in Betti Geometric Langlands by Yun, Zhiwei

“…In particular, we establish the “automorphic to Galois” direction in the Betti Geometric Langlands correspondence—to each indecomposable automorphic sheaf, we attach a dual group local system—and define the Betti version of V. …”
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ℤ/����ℤ-graded Lie algebras and perverse sheaves, III: Graded double affine Hecke algebra by Lusztig, George, Yun, Zhiwei

“…Theory 21 (2017), pp. 277-321], we attach a graded DAHA and construct its action on the direct sum of spiral inductions in that block. …”
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Self-sustained nonlinear waves in traffic flow by Flynn, Morris R., Kasimov, Aslan R., Nave, Jean-Christophe, Rosales, Rodolfo R., Seibold, Benjamin

“…In analogy to gas-dynamical detonation waves, which consist of a shock with an attached exothermic reaction zone, we consider herein nonlinear traveling wave solutions to the hyperbolic (“inviscid”) continuum traffic equations. …”
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Semistable reduction for overconvergent F-isocrystals, IV: Local semistable reduction at nonmonomial valuations by Kedlaya, Kiran S.

“…We do this by studying the variation of some numerical invariants attached to p-adic differential modules, analogous to the irregularity of a complex meromorphic connection. …”
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On elliptic Calogero–Moser systems for complex crystallographic reflection groups by Felder, Giovanni, Ma, Xiaoguang, Veselov, Alexander, Etingof, Pavel I.

“…To every irreducible finite crystallographic reflection group (i.e., an irreducible finite reflection group G acting faithfully on an abelian variety X), we attach a family of classical and quantum integrable systems on X (with meromorphic coefficients). …”
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