April 10
This day in history:
- 1710 – The Statute of Anne, the first law regulating copyright, comes into force in Great Britain.
- 1809 – Napoleonic Wars: The War of the Fifth Coalition begins when forces of the Austrian Empire invade Bavaria.
- 1821 – Greek War of Independence: the island of Psara joins the Greek struggle for independence.
- 1916 – The Professional Golfers' Association of America (PGA) is created in New York City.
Births:
- 1940 – Gloria Hunniford, British radio and television host
- 1974 – Eric Greitens, American soldier, author and politician
- 1704 – Benjamin Heath, English scholar and author (d. 1766)
Deaths:
- 1969 – Harley Earl, American businessman (b. 1893)
- 1991 – Kevin Peter Hall, American actor (b. 1955)
- 1983 – Issam Sartawi, Palestinian activist (b. 1935)
Holidays:
- Day of the Builder (Azerbaijan)
- Feast of the Third Day of the Writing of the Book of the Law (Thelema)
- Siblings Day (International observance)
Random Article of the day:
Monomial representation
In the mathematical fields of representation theory and group theory, a linear representation
ρ
{\displaystyle \rho }
(rho) of a group
G
{\displaystyle G}
is a monomial representation if there is a finite-index subgroup
H
{\displaystyle H}
and a one-dimensional linear representation
σ
{\displaystyle \sigma }
of
H
{\displaystyle H}
, such that
ρ
{\displaystyle \rho }
is equivalent to the induced representation
I
n
d
H
G
σ
{\displaystyle \mathrm {Ind} {H}{G{\sigma }}}
.
Alternatively, one may define it as a representation whose image is in the monomial matrices.
Here for example
G
{\displaystyle G}
and
H
{\displaystyle H}
may be finite groups, so that induced representation has a classical sense. The monomial representation is only a little more complicated than the permutation representation of
G
{\displaystyle G}
on the cosets of
H
{\displaystyle H}
. It is necessary only to keep track of scalars coming from
σ
{\displaystyle \sigma }
applied to elements of
H
{\displaystyle H}
.
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