A matrix $A$ over the field of real numbers is **totally positive** (resp. **totally nonnegative**) if every minor (= determinant of any submatrix) is a positive (resp. nonnegative) real number. Total positivity implies a number of remarkable properties; for example all eigenvalues are distinct and positive. George Lusztig discovered that this classical total positivity is a related to more general **total positivity** phenomena in the theory of Lie groups and quantum groups.

- George Lusztig,
*Total positivity in reductive groups*, In: Brylinski, JL., Brylinski, R., Guillemin, V., Kac, V. (eds) Lie Theory and Geometry. Progress in Mathematics**123**; BirkhĂ¤user 1994 doi - cluster algebra
- many lecture notes listed at a minicourse page on total positivity
- M. Skandera,
*Introductory notes on total positivity*, ps, June 2003. - Yuji Kodama, Lauren Williams,
*KP solitons and total positivity for the Grassmannian*, arXiv:1106.0023

category: algebra

Last revised on September 17, 2023 at 13:57:13. See the history of this page for a list of all contributions to it.