Quasi-parabolic subgroups of the Weyl group of type D

Jun Hu

doi:10.1016/j.ejc.2005.12.001

Quasi-parabolic subgroups of the Weyl group of type D

Jun Hu^*

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We consider quasi-parabolic subgroups of the Weyl group W (D_n) of type D_n, which are intersections of W (D_n) with quasi-parabolic subgroups of the Weyl group W (B_n) of type B_n (see [J. Du, L. Scott, The q-Schur² algebra, Trans. Amer. Math. Soc. 352 (2000) 4325-4353] and [C.K. Mak, Quasi-parabolic subgroups of G (m, 1, r), J. Algebra 246 (2001) 471-490]). We study the properties of cosets of these subgroups in W (D_n). A length function formula of type D_n is derived. A complete set of right coset representatives of these subgroups is constructed. We show that each of these representatives is of minimum length (with respect to both type B_n and type D_n length functions) in the coset it belongs to. Characterizations of these representatives via certain tableaux are given. Finally, a complete set of double coset representatives of quasi-parabolic subgroups in W (D_n) is also obtained, and we show that each of these representatives is of minimum length with respect to type B_n length functions in the double coset it belongs to.

Original language	English
Pages (from-to)	807-821
Number of pages	15
Journal	European Journal of Combinatorics
Volume	28
Issue number	3
DOIs	https://doi.org/10.1016/j.ejc.2005.12.001
Publication status	Published - Apr 2007

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title = "Quasi-parabolic subgroups of the Weyl group of type D",

abstract = "We consider quasi-parabolic subgroups of the Weyl group W (Dn) of type Dn, which are intersections of W (Dn) with quasi-parabolic subgroups of the Weyl group W (Bn) of type Bn (see [J. Du, L. Scott, The q-Schur2 algebra, Trans. Amer. Math. Soc. 352 (2000) 4325-4353] and [C.K. Mak, Quasi-parabolic subgroups of G (m, 1, r), J. Algebra 246 (2001) 471-490]). We study the properties of cosets of these subgroups in W (Dn). A length function formula of type Dn is derived. A complete set of right coset representatives of these subgroups is constructed. We show that each of these representatives is of minimum length (with respect to both type Bn and type Dn length functions) in the coset it belongs to. Characterizations of these representatives via certain tableaux are given. Finally, a complete set of double coset representatives of quasi-parabolic subgroups in W (Dn) is also obtained, and we show that each of these representatives is of minimum length with respect to type Bn length functions in the double coset it belongs to.",

author = "Jun Hu",

year = "2007",

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doi = "10.1016/j.ejc.2005.12.001",

language = "English",

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pages = "807--821",

journal = "European Journal of Combinatorics",

issn = "0195-6698",

publisher = "Academic Press",

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}

TY - JOUR

T1 - Quasi-parabolic subgroups of the Weyl group of type D

AU - Hu, Jun

PY - 2007/4

Y1 - 2007/4

N2 - We consider quasi-parabolic subgroups of the Weyl group W (Dn) of type Dn, which are intersections of W (Dn) with quasi-parabolic subgroups of the Weyl group W (Bn) of type Bn (see [J. Du, L. Scott, The q-Schur2 algebra, Trans. Amer. Math. Soc. 352 (2000) 4325-4353] and [C.K. Mak, Quasi-parabolic subgroups of G (m, 1, r), J. Algebra 246 (2001) 471-490]). We study the properties of cosets of these subgroups in W (Dn). A length function formula of type Dn is derived. A complete set of right coset representatives of these subgroups is constructed. We show that each of these representatives is of minimum length (with respect to both type Bn and type Dn length functions) in the coset it belongs to. Characterizations of these representatives via certain tableaux are given. Finally, a complete set of double coset representatives of quasi-parabolic subgroups in W (Dn) is also obtained, and we show that each of these representatives is of minimum length with respect to type Bn length functions in the double coset it belongs to.

AB - We consider quasi-parabolic subgroups of the Weyl group W (Dn) of type Dn, which are intersections of W (Dn) with quasi-parabolic subgroups of the Weyl group W (Bn) of type Bn (see [J. Du, L. Scott, The q-Schur2 algebra, Trans. Amer. Math. Soc. 352 (2000) 4325-4353] and [C.K. Mak, Quasi-parabolic subgroups of G (m, 1, r), J. Algebra 246 (2001) 471-490]). We study the properties of cosets of these subgroups in W (Dn). A length function formula of type Dn is derived. A complete set of right coset representatives of these subgroups is constructed. We show that each of these representatives is of minimum length (with respect to both type Bn and type Dn length functions) in the coset it belongs to. Characterizations of these representatives via certain tableaux are given. Finally, a complete set of double coset representatives of quasi-parabolic subgroups in W (Dn) is also obtained, and we show that each of these representatives is of minimum length with respect to type Bn length functions in the double coset it belongs to.

UR - https://www.scopus.com/pages/publications/33751427946

U2 - 10.1016/j.ejc.2005.12.001

DO - 10.1016/j.ejc.2005.12.001

M3 - Article

AN - SCOPUS:33751427946

SN - 0195-6698

VL - 28

SP - 807

EP - 821

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

IS - 3

ER -

Quasi-parabolic subgroups of the Weyl group of type D

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