Minimal length elements of extended affine Weyl groups

Xuhua He Sian Nie

Representation Theory mathscidoc:1912.43196

Compositio Mathematica, 150, (11), 1903-1927, 2014.11
Let W be an extended affine Weyl group. We prove that the minimal length elements W of any conjugacy class W of W satisfy some nice properties, generalizing results of Geck and Pfeiffer [<i>On the irreducible characters of Hecke algebras</i>, Adv. Math. <b>102</b> (1993), 7994] on finite Weyl groups. We also study a special class of conjugacy classes, the straight conjugacy classes. These conjugacy classes are in a natural bijection with the Frobenius-twisted conjugacy classes of some W -adic group and satisfy additional interesting properties. Furthermore, we discuss some applications to the affine Hecke algebra W
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  title={Minimal length elements of extended affine Weyl groups},
  author={Xuhua He, and Sian Nie},
  booktitle={Compositio Mathematica},
Xuhua He, and Sian Nie. Minimal length elements of extended affine Weyl groups. 2014. Vol. 150. In Compositio Mathematica. pp.1903-1927.
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