In his monograph Arthur (The endoscopic classification of representations: orthogonal and symplectic groups, Colloquium Publications, American Mathematical Society, Providence, 2013) characterizes the L-packets of quasisplit symplectic groups and orthogonal groups. By extending his work, we characterize the L-packets for the corresponding similitude groups with desired properties. In particular, we show these packets satisfy the conjectural endoscopic character identities.

The classification and lattice model construction of symmetry-protected topological (SPT) phases in interacting fermion systems are very interesting but challenging. In this paper, we give a systematic fixed-point wave function construction of fermionic SPT (FSPT) states for generic fermionic symmetry group G_f = \mathbb{Z}^f_2 ×_{ω_2} G_b which is a central extension of bosonic symmetry group Gb (may contain time-reversal symmetry) by the fermion parity symmetry group \mathbb{Z}^f_2 = {1,P_f}. Our construction is based on the concept of an equivalence class of finite-depth fermionic symmetric local unitary transformations and decorating symmetry domain wall picture, subjected to certain obstructions. We also discuss the systematical construction and classification of boundary anomalous SPT states which leads to a trivialization of the corresponding bulk FSPT states. Thus, we conjecture that the obstruction-free and trivialization-free constructions naturally lead to a classification of FSPT phases. Each fixed-point wave function admits an exactly solvable commuting-projector Hamiltonian. We believe that our classification scheme can be generalized to point and space group symmetry as well as continuum Lie group symmetry.

No abstract uploaded!

No abstract uploaded!

No abstract uploaded!