Geodesic
E-Polynomials of Generic $\mathbf {\operatorname {\mathrm {GL}}_n\rtimes \!\!\sigma \!>\!}~$-Character Varieties: Branched Case
Forum of Mathematics, Sigma, Tome 11 (2023)

Voir la notice de l'article provenant de la source Cambridge University Press

For any branched double covering of compact Riemann surfaces, we consider the associated character varieties that are unitary in the global sense, which we call $\operatorname {\mathrm {GL}}_n\rtimes \!\!\sigma {>}$-character varieties. We restrict the monodromies around the branch points to generic semi-simple conjugacy classes contained in $\operatorname {\mathrm {GL}}_n\sigma $ and compute the E-polynomials of these character varieties using the character table of $\operatorname {\mathrm {GL}}_n(q)\rtimes \!\!\sigma \!>\!$. The result is expressed as the inner product of certain symmetric functions associated to the wreath product $(\mathbb {Z}/2\mathbb {Z})^N\rtimes \mathfrak {S}_N$. We are then led to a conjectural formula for the mixed Hodge polynomial, which involves (modified) Macdonald polynomials and wreath Macdonald polynomials. 
@article{10_1017_fms_2023_119,
     author = {Cheng Shu},
     title = {E-Polynomials of {Generic} $\mathbf {\operatorname {\mathrm {GL}}_n\rtimes \!<\!\sigma \!>\!}~${-Character} {Varieties:} {Branched} {Case}},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {11},
     year = {2023},
     doi = {10.1017/fms.2023.119},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2023.119/}
}
TY  - JOUR
AU  - Cheng Shu
TI  - E-Polynomials of Generic $\mathbf {\operatorname {\mathrm {GL}}_n\rtimes \!<\!\sigma \!>\!}~$-Character Varieties: Branched Case
JO  - Forum of Mathematics, Sigma
PY  - 2023
VL  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1017/fms.2023.119/
DO  - 10.1017/fms.2023.119
LA  - en
ID  - 10_1017_fms_2023_119
ER  - 
%0 Journal Article
%A Cheng Shu
%T E-Polynomials of Generic $\mathbf {\operatorname {\mathrm {GL}}_n\rtimes \!<\!\sigma \!>\!}~$-Character Varieties: Branched Case
%J Forum of Mathematics, Sigma
%D 2023
%V 11
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1017/fms.2023.119/
%R 10.1017/fms.2023.119
%G en
%F 10_1017_fms_2023_119
Cheng Shu. E-Polynomials of Generic $\mathbf {\operatorname {\mathrm {GL}}_n\rtimes \!<\!\sigma \!>\!}~$-Character Varieties: Branched Case. Forum of Mathematics, Sigma, Tome 11 (2023). doi: 10.1017/fms.2023.119

Cité par Sources :