Singular Loci of Schubert Varieties is a unique work at the crossroads of representation theory
algebraic geometry and combinatorics. Over the past 20 years many research articles have been
written on the subject in notable journals. In this work Billey and Lakshmibai have recreated
and restructured the various theories and approaches of those articles and present a clearer
understanding of this important subdiscipline of Schubert varieties - namely singular loci. The
main focus therefore is on the computations for the singular loci of Schubert varieties and
corresponding tangent spaces. The methods used include standard monomial theory the nil Hecke
ring and Kazhdan-Lusztig theory. New results are presented with sufficient examples to
emphasize key points. A comprehensive bibliography index and tables - the latter not to be
found elsewhere in the mathematics literature - round out this concise work. After a good
introduction giving background material the topics are presented in a systematic fashion to
engage a wide readership of researchers and graduate students.
