Linear representation theory of special linear group of degree two over a finite field
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This article gives specific information, namely, linear representation theory, about a family of groups, namely: special linear group of degree two.
View linear representation theory of group families | View other specific information about special linear group of degree two
This article describes the linear representation theory of the special linear group of degree two over a finite field. The order (size) of the field is , and the characteristic prime is
.
is a power of
. We denote the group as
or
.
See also the linear representation theories of: general linear group of degree two, projective general linear group of degree two, and projective special linear group of degree two.
For linear representation theory in characteristics that divide the order of the group, refer:
- Modular representation theory of special linear group of degree two over a finite field in its defining characteristic: In characteristic
, same as the field characteristic.
- (Modular representation theory in other characteristics that divide
or
-- link to be added)
Summary
Item | Value |
---|---|
degrees of irreducible representations over a splitting field (such as ![]() ![]() |
Case ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() Case ![]() ![]() ![]() ![]() ![]() ![]() |
number of irreducible representations | Case ![]() ![]() ![]() ![]() See number of irreducible representations equals number of conjugacy classes, element structure of special linear group of degree two over a finite field#Conjugacy class structure |
quasirandom degree (minimum degree of nontrivial irreducible representation) | Case ![]() ![]() Case ![]() ![]() |
maximum degree of irreducible representation over a splitting field | ![]() ![]() ![]() ![]() |
lcm of degrees of irreducible representations over a splitting field | Case ![]() Case ![]() ![]() ![]() Case ![]() ![]() |
sum of squares of degrees of irreducible representations over a splitting field | ![]() |