Hi, sometimes I check Google Scholar and Arxiv in order to be updated for new papers in our field and it seems that this extension from Takeji Ueda totally avoided my radar.
https://arxiv.org/pdf/2105.00247.pdf
To be honest I didn't have time to give it more than a quick look. It actually reminds me a lot of that approach with q-analogs worked out by Vladimir Reshetnikov in 2017. I remember Daniel and James being somehow active on those MO questions so they know better than me for sure. I didn't see any reference to those MO conversations, only to the older Hooshmand, Kouznetzov and Paulsen-Cowjill. So I can't conclude if original results are presented or the author just grabbed ideas in the air and polished the details and completed the proofs. I post here the link for future references.
https://arxiv.org/pdf/2105.00247.pdf
To be honest I didn't have time to give it more than a quick look. It actually reminds me a lot of that approach with q-analogs worked out by Vladimir Reshetnikov in 2017. I remember Daniel and James being somehow active on those MO questions so they know better than me for sure. I didn't see any reference to those MO conversations, only to the older Hooshmand, Kouznetzov and Paulsen-Cowjill. So I can't conclude if original results are presented or the author just grabbed ideas in the air and polished the details and completed the proofs. I post here the link for future references.
Mother Law \(\sigma^+\circ 0=\sigma \circ \sigma^+ \)
\({\rm Grp}_{\rm pt} ({\rm RK}J,G)\cong \mathbb N{\rm Set}_{\rm pt} (J, \Sigma^G)\)