TY - JOUR

T1 - Tits construction and Rost invariant

AU - Geldhauser, Nikita

AU - Петров, Виктор Александрович

PY - 2024/12/1

Y1 - 2024/12/1

N2 - We show a Springer type theorem for the variety of parabolic subgroups of type 1, 2, 6 for all groups of type E6. As far as we know this gives the first example for the validity of the Springer theorem for projective homogeneous varieties of type 2E6 different from varieties of Borel subgroups. The proof combines several topics, notably the Rost invariant, a Tits construction, Cartan’s symmetric spaces and indirectly the structure of the Chow motives of projective homogeneous varieties of exceptional type.

AB - We show a Springer type theorem for the variety of parabolic subgroups of type 1, 2, 6 for all groups of type E6. As far as we know this gives the first example for the validity of the Springer theorem for projective homogeneous varieties of type 2E6 different from varieties of Borel subgroups. The proof combines several topics, notably the Rost invariant, a Tits construction, Cartan’s symmetric spaces and indirectly the structure of the Chow motives of projective homogeneous varieties of exceptional type.

KW - 14C15

KW - 20G15

KW - Linear algebraic groups

KW - Symmetric spaces

KW - Twisted flag varieties

UR - https://www.mendeley.com/catalogue/d41c44f3-f03b-3d96-adb0-88eeefe72992/

U2 - 10.1007/s40879-024-00787-5

DO - 10.1007/s40879-024-00787-5

M3 - Article

VL - 10

JO - European Journal of Mathematics

JF - European Journal of Mathematics

SN - 2199-675X

IS - 4

M1 - 76

ER -