TY - JOUR
T1 - Virtual hodge polynomials of the moduli spaces of representations of degree 2 for free monoids
AU - Nakamoto, Kazunori
AU - Torii, Takeshi
N1 - Funding Information:
The first author was partially supported by JSPS KAKENHI Grant Number 23540044, 15K04814. The second author was partially supported by JSPS KAKENHI Grant Number 22540087, 25400092.
Publisher Copyright:
© 2016, Tokyo Institute of Technology. All rights reserved.
PY - 2016/3/25
Y1 - 2016/3/25
N2 - In this paper we study the topology of the moduli spaces of representations of degree 2 for free monoids. We calculate the virtual Hodge polynomials of the character varieties for several types of 2-dimensional representations. Furthermore, we count the number of isomorphism classes for each type of 2-dimensional representations over any finite field Fq, and show that the number coincides with the virtual Hodge polynomial evaluated at q.
AB - In this paper we study the topology of the moduli spaces of representations of degree 2 for free monoids. We calculate the virtual Hodge polynomials of the character varieties for several types of 2-dimensional representations. Furthermore, we count the number of isomorphism classes for each type of 2-dimensional representations over any finite field Fq, and show that the number coincides with the virtual Hodge polynomial evaluated at q.
KW - Character variety
KW - Moduli of representations
KW - Representation variety
KW - Virtual hodge polynomial
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U2 - 10.2996/kmj/1458651693
DO - 10.2996/kmj/1458651693
M3 - Article
AN - SCOPUS:84961639801
SN - 0386-5991
VL - 39
SP - 80
EP - 109
JO - Kodai Mathematical Journal
JF - Kodai Mathematical Journal
IS - 1
ER -