Kazhdan-Lusztig Cells in Affine Weyl Groups of Rank 2

Guilhot, Jeremie

doi:10.1093/imrn/rnp243

Cited by 13 publications

(32 citation statements)

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“…In this section we recall the decomposition of

{\tilde{G}}_{2}

into right cells and two‐sided cells for all choices of parameters

false(a, b false) \in {double-struckN}^{2}

from . We also recall some ‘cell factorisation’ properties for the infinite two‐sided cells from .…”

Section: Kazhdan–lusztig Cells In Type G∼2mentioning

confidence: 99%

“…In the case of

{\tilde{G}}_{2}

, we construct a balanced system of cell representations for each parameter regime. Our starting point is the partition of

W

into Kazhdan–Lusztig cells that was proved by the first author in . It turns out that the representations associated to finite cells naturally give rise to balanced representations and so most of our work is concerned with the infinite cells.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A proof of Lusztig's conjectures for affine type G2 with arbitrary parameters

Guilhot

Parkinson

2018

Proc. London Math. Soc.

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We prove Lusztig's conjectures P1–P15 for the affine Weyl group of type G∼2 for all choices of parameters. Our approach to compute Lusztig's bolda‐function is based on the notion of a ‘balanced system of cell representations’ for the Hecke algebra. We show that for arbitrary Coxeter type the existence of balanced system of cell representations is sufficient to compute the bolda‐function and we explicitly construct such a system in type G∼2 for arbitrary parameters. We then investigate the connection between Kazhdan–Lusztig cells and the Plancherel theorem in type G∼2, allowing us to prove P1 and determine the set of Duflo involutions. From there, the proof of the remaining conjectures follows very naturally, essentially from the combinatorics of Weyl characters of types G2 and A1, along with some explicit computations for the finite cells.

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“…In this section we recall the decomposition of

{\tilde{G}}_{2}

into right cells and two‐sided cells for all choices of parameters

false(a, b false) \in {double-struckN}^{2}

from . We also recall some ‘cell factorisation’ properties for the infinite two‐sided cells from .…”

Section: Kazhdan–lusztig Cells In Type G∼2mentioning

confidence: 99%

“…In the case of

{\tilde{G}}_{2}

, we construct a balanced system of cell representations for each parameter regime. Our starting point is the partition of

W

Section: Introductionmentioning

confidence: 99%

A proof of Lusztig's conjectures for affine type G2 with arbitrary parameters

Guilhot

Parkinson

2018

Proc. London Math. Soc.

View full text Add to dashboard Cite

show abstract

“…(1)-(2) follow by 4.1-4.2 and Proposition 2.8 (3). For (3), we need only to show that F 1 is contained in an rcc of E k1 2n−k .…”

Section: 2mentioning

confidence: 95%

“…6.7. Let F 1 = { [4,5,6], [0,4,5], [−1, 4, 6], [−2, 5, 6], [−2, −1, 0], [−1, 0, 4], [−2, 0, 5], [−2, −1, 6]}, F 2 = { [4,1,5], [0,4,2], [2,4,6], [3,5,6], [2,0,4], [0, 3,5], [−1, 3, 6], [−1, 1, 4], [−2, 1, 5], [−1, 3, 0], [−2, −1, 1], [−2, 0, 2]}, F 3 = { [2,1,4], [3,1,5], [0, 3,2], [−1, 3, 1]}. We see by 3.3 that any x ∈ F 2 3 satisfying (a) (respectively, (b), (c)) in (6.6.1) is in an lcc of E 2 3 containing some element of F 1 (respectively, F 2 , F 3 ).…”

Section: The Cells In the Weighted Coxeter Group ( C 3 )mentioning

confidence: 99%