From the schematic pictured this is a 4-burner cooktop with one burner rated at 1400 W, another at 1600 W so 3000 W total for those. Another burner is 1200 W, giving 4200 W total. What about the fourth burner?
Since the schematic shows L1, L2 we know this is powered at 240 V. What is the total wattage of all the burners? How many are there? The maximum current would be at least 4200 W / 240 V = 17.5 A. A fourth burner would put the total maximum current well past 20 A. To power this cooktop it looks like you should have a 30 A breaker with AWG 8 aluminum wire (or 10 AWG copper).
The fine-stranded conductor in the three leads on the cooktop wiring are labeled 10AWG (stranded copper, tinned? Or fine stranded aluminum (if there is such a thing)? indicateing the expected maximum current is over 20 A. But what do the specs state?
It is possible the cooktop has circuitry that automatically limits the total power to less than the sum of the maxima of the four burners. (My 2-burner induction cooktop has two burners rated at 1800 W each at 120 V, but it will not let both run at full power simultaneously. The rated total power is 1800 W at 120 V (so 15 A) and the specs allow it to operate on a 20 A circuit. What are the power specifications for this four burner cooktop?
Can you read the writing on the wire sheath of the house wire and report back the gauge of the wire?
I would expect the breaker for this circuit would be a 2-pole 20 A breaker or a 30 A breaker. Is that what is in the electrical panel? If the wire is #8 aluminum, then you might have a 30 A 2-pole breaker. Do the installation instructions for the cooktop specify the breaker size?
There will be a requirement for aluminum rated connectors. If the house wire is AWG 10, then the relatively cheap AlumiConn connectors would be rated for this connection.
The Ideal Purple twist on connectors are legal to use AFIK, (but not sure about the limit on wire size) but at least one expert on aluminum wiring, Jesse Aronson, thinks the Ideal Purple twist on connectors are not reliable.
Everyone agrees that AlumiConns (King Innovation) are the gold standard for connections up to #10 solid aluminum to copper or to other aluminum. You would need three of these and they are probably available at a big box. Two of the AlumiConns could be the two port (for L1 and L2) and you would want a 3-port for the ground so you could have a third wire of #12 copper to ground the box.
But if the AlumiConns come in a package of say 4, then you could use the 3-port for all three connections and just leave one port unused. If you decide to use the AlumiConns say so and we will give you instructions on how to use them.
AFIK the AlumiConns cannot accept #8 solid aluminum condictor so if you do have #8 wire you will have to use a different and more expensive connector.