Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

USEFUL OPERATORS ON REPRESENTATIONS OF THE RATIONAL CHEREDNIK ALGEBRA OF TYPE 𝔰𝔩 n

  • Shin, Gicheol (Department of Mathematics Education, Korea National University of Education)
  • Received : 2018.11.14
  • Accepted : 2019.03.12
  • Published : 2019.06.25
Download PDF
⟨ Previous Next ⟩

Abstract

Let n denote an integer greater than 2 and let c denote a nonzero complex number. In this paper, we introduce a family of elements of the rational Cherednik algebra $H^{sl_n}(c)$ of type $sl_n$, which are analogous to the Dunkl-Cherednik elements of the rational Cherednik algebra $H^{gl_n}(c)$ of type $gl_n$. We also introduce the raising and lowering element of $H^{sl_n}(c)$ which are useful in the representation theory of the algebra $H^{sl_n}(c)$, and provide simple results related to these elements.

Keywords

References

  1. Damien Calaque, Benjamin Enriquez, and Pavel Etingof, Universal KZB equations: the elliptic case, Algebra, arithmetic, and geometry: in honor of Yu. I. Manin. Vol. I (2009), 165-266.
  2. Pavel Etingof and Victor Ginzburg, Symplectic re ection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism, Invent. Math. 147(2) (2002), 243-348. https://doi.org/10.1007/s002220100171
  3. Ivan Cherednik, A unification of Knizhnik-Zamolodchikov and Dunkl operators via affine Hecke algebras, Invent. Math. 106(2) (1991), 411-431. https://doi.org/10.1007/BF01243918
  4. Ivan Cherednik, Double affine Hecke algebras and difference Fourier transforms, Invent. Math. 152(2) (2003), 213-303. https://doi.org/10.1007/s00222-002-0240-0
  5. Takeshi Suzuki, Rational and trigonometric degeneration of the double affine Hecke algebra of type A, Int. Math. Res. Not. 37 (2005), 2249-2262. https://doi.org/10.1155/IMRN.2005.2249
  6. Takeshi Suzuki and Monica Vazirani, Tableaux on periodic skew diagrams and irreducible representations of the double affine Hecke algebra of type A, Int. Math. Res. Not. 27 (2005), 1621-1656