Double Affine Hecke Algebras
By I. Cherednik. 2005
383 citations recorded by the source corpus.
Subfields: Algebra and Number Theory
View Paper: https://www.semanticscholar.org/paper/1e7b67b619bd81f742c81b4afb10f3264826ec7a
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In Algebra and Number Theory
- Thomas Lam
- Mark Shimozono
- I. Gordon
- E. Gorsky
- Raphaël Rouquier
- Anne Schilling
- Pavel Etingof
- Jennifer Morse
Citations in the corpus
- Affine permutations and rational slope parking functions (2014, neutral): “This th eory is quite elaborate and far beyond the scope of this paper, so we refer the reader to Cherednik’s book [6] for all details.”
- Gauge Theories and Macdonald Polynomials (2011, background): “[42, 58] for pedagogic expositions and [59] for a brief review),”
- Cherednik algebras, W-algebras and the equivariant cohomology of the moduli space of instantons on A2 (2012, background): “11) Hn = Hn,A ⊗A K, SHn = SHn,A ⊗A K, We have an A-basis of Hn,A given by [10] (7.”
- q-Schur algebras and complex reflection groups, I (2005, methodology): “11 via the work of Suzuki [55], which relates representations of rational Cherednik algebras of type A with representations at negative level of affine Lie algebras of type A.”
- A combinatorial formula for non-symmetric Macdonald polynomials (2006, neutral): “A (n) D es( )= D non-attacking x j j( 1)m ( )tp( )+ jInv( )j:”
- DAHA and iterated torus knots (2014, methodology): “Following [10], we use the PBW theorem to express any H 2 HH in the form P a;w;b ca;w;bXaTwYb for w 2W and a; b 2 P (this presentation is unique).”
- Symplectic reflection algebras (2007, background): “These include positive characteristic, [16], [102], [24]; continuous Hecke algebras, [49], [115]; generalisations of Schur– Weyl duality, [84], [85], [86]; connections with affine Lie algebras, [2]; Cherednik algebras for varieties with group actions, [46]; relations with Hopf algebras, [4]; real al”
- The importance of the Selberg integral (2007, background): “Cherednik gave a uniform proof for all reduced root systems based on his theory of double affine Hecke algebras [29, 30, 31, 111].”
- Refined knot invariants and Hilbert schemes (2013, methodology): “Following [14], we will define the double affine Hecke algebra (DAHA) of typeAN .”