Roger Wolcott Richardson
Encyclopedia
Roger Wolcott Richardson (30 May 1930 – 15 June 1993) was a mathematician noted for his work in representation theory
and geometry
. He was born in Baton Rouge, Louisiana
, and educated at Louisiana State University
, Harvard University
and University of Michigan, Ann Arbor where he obtained a Ph.D. under the supervision of Hans Samelson
. He emigrated in 1970, and subsequently worked in the United Kingdom
and Australia
.
Richardson’s best known result states that if P is a parabolic subgroup of a reductive group
, then P has a dense orbit on its nilradical, i.e., one whose closure is the whole space. This orbit is now universally known as the Richardson orbit .
Representation theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studiesmodules over these abstract algebraic structures...
and geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
. He was born in Baton Rouge, Louisiana
Baton Rouge, Louisiana
Baton Rouge is the capital of the U.S. state of Louisiana. It is located in East Baton Rouge Parish and is the second-largest city in the state.Baton Rouge is a major industrial, petrochemical, medical, and research center of the American South...
, and educated at Louisiana State University
Louisiana State University
Louisiana State University and Agricultural and Mechanical College, most often referred to as Louisiana State University, or LSU, is a public coeducational university located in Baton Rouge, Louisiana. The University was founded in 1853 in what is now known as Pineville, Louisiana, under the name...
, Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
and University of Michigan, Ann Arbor where he obtained a Ph.D. under the supervision of Hans Samelson
Hans Samelson
Hans Samelson was a German American mathematician who worked in differential geometry, topology and the theory of Lie groups and Lie algebras—important in describing the symmetry of analytical structures....
. He emigrated in 1970, and subsequently worked in the United Kingdom
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...
and Australia
Australia
Australia , officially the Commonwealth of Australia, is a country in the Southern Hemisphere comprising the mainland of the Australian continent, the island of Tasmania, and numerous smaller islands in the Indian and Pacific Oceans. It is the world's sixth-largest country by total area...
.
Richardson’s best known result states that if P is a parabolic subgroup of a reductive group
Reductive group
In mathematics, a reductive group is an algebraic group G over an algebraically closed field such that the unipotent radical of G is trivial . Any semisimple algebraic group is reductive, as is any algebraic torus and any general linear group...
, then P has a dense orbit on its nilradical, i.e., one whose closure is the whole space. This orbit is now universally known as the Richardson orbit .
External links
- Mathematical ReviewsMathematical ReviewsMathematical Reviews is a journal and online database published by the American Mathematical Society that contains brief synopses of many articles in mathematics, statistics and theoretical computer science.- Reviews :...
analysis