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The 26D irrep of F4 decomposes into 3 irreps of Spin(9), of dimensions 1, 9, and 16. The 1D factor means Spin(9) stabilizes a vector in the...
https://mathstodon.xyz/@Mecejide...The 26D irrep of F4 decomposes into 3 irreps of Spin(9), of dimensions 1, 9, and 16. The 1D factor means Spin(9) stabilizes a vector in the irrep, and the orbit of such a point must be F4/Spin(9). What this all means is that F4/Spin(9), AKA the Cayley plane, has a homogeneous embedding into R^26.
16.11.2025 05:56The 26D irrep of F4 decomposes into 3 irreps of Spin(9), of dimensions 1, 9, and 16. The 1D factor means Spin(9) stabilizes a vector in the...https://mathstodon.xyz/@Mecejide...
I recently (re)discovered a nice description of the E₇ root system. Its vector shapes are all sign changes and cyclic permutations of...
https://mathstodon.xyz/@Mecejide...I recently (re)discovered a nice description of the E₇ root system. Its vector shapes are all sign changes and cyclic permutations of (1,0,0,0,0,0,0) and (½,½,½,0,½,0,0).
2.1.2024 02:29I recently (re)discovered a nice description of the E₇ root system. Its vector shapes are all sign changes and cyclic permutations of...https://mathstodon.xyz/@Mecejide...
Why the retroantiprismatosnub dishecatonicosachoron is my favorite mathematical object:• It is the only known uniform polychoron aside...
https://mathstodon.xyz/@Mecejide...Why the retroantiprismatosnub dishecatonicosachoron is my favorite mathematical object:
• It is the only known uniform polychoron aside from the prisms that has snub polyhedra as cells.
• It is the only known uniform polychoron with pairs of cells that share two faces.
https://mathstodon.xyz/@Mecejide...
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