# Kazhdan–Lusztig basis and a geometric filtration of an affine Hecke algebra, II

Journal of the European Mathematical Society (2011)

- Volume: 013, Issue: 1, page 207-217
- ISSN: 1435-9855

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topXi, Nanhua. "Kazhdan–Lusztig basis and a geometric filtration of an affine Hecke algebra, II." Journal of the European Mathematical Society 013.1 (2011): 207-217. <http://eudml.org/doc/277162>.

@article{Xi2011,

abstract = {An affine Hecke algebras can be realized as an equivariant $K$-group of the corresponding Steinberg variety. This gives rise naturally to some two-sided ideals of the affine Hecke algebra by means of the closures of nilpotent orbits of the corresponding Lie algebra. In this paper we will show that the two-sided ideals are in fact the two-sided ideals of the affine Hecke algebra defined through two-sided cells of the corresponding affine Weyl group after the two-sided ideals are tensored by $\mathbb \{Q\}$. This proves a weak form of a conjecture of Ginzburg proposed in 1987.},

author = {Xi, Nanhua},

journal = {Journal of the European Mathematical Society},

keywords = {affine Hecke algebra; two-sided cell; two-sided ideal; affine Weyl groups; reductive algebraic groups; Kazhdan-Lusztig bases; nilpotent orbits; affine Hecke algebras; two-sided cells; two-sided ideals; affine Weyl groups; reductive algebraic groups; Kazhdan-Lusztig bases; nilpotent orbits},

language = {eng},

number = {1},

pages = {207-217},

publisher = {European Mathematical Society Publishing House},

title = {Kazhdan–Lusztig basis and a geometric filtration of an affine Hecke algebra, II},

url = {http://eudml.org/doc/277162},

volume = {013},

year = {2011},

}

TY - JOUR

AU - Xi, Nanhua

TI - Kazhdan–Lusztig basis and a geometric filtration of an affine Hecke algebra, II

JO - Journal of the European Mathematical Society

PY - 2011

PB - European Mathematical Society Publishing House

VL - 013

IS - 1

SP - 207

EP - 217

AB - An affine Hecke algebras can be realized as an equivariant $K$-group of the corresponding Steinberg variety. This gives rise naturally to some two-sided ideals of the affine Hecke algebra by means of the closures of nilpotent orbits of the corresponding Lie algebra. In this paper we will show that the two-sided ideals are in fact the two-sided ideals of the affine Hecke algebra defined through two-sided cells of the corresponding affine Weyl group after the two-sided ideals are tensored by $\mathbb {Q}$. This proves a weak form of a conjecture of Ginzburg proposed in 1987.

LA - eng

KW - affine Hecke algebra; two-sided cell; two-sided ideal; affine Weyl groups; reductive algebraic groups; Kazhdan-Lusztig bases; nilpotent orbits; affine Hecke algebras; two-sided cells; two-sided ideals; affine Weyl groups; reductive algebraic groups; Kazhdan-Lusztig bases; nilpotent orbits

UR - http://eudml.org/doc/277162

ER -

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